Simplifying rational expressions

Friends! In this article we are going to see the way of solving any complex rational expression and why these rational expressions are said to be a complex type of mathematical problem. Those students who are perusing in 9th standard often face the rational expression problems. There are various online tutoring websites that offers several online solvers. These online solvers are generally computer coded program s which runs on the Internet platform. Online solver prefers when any math query is need to be solved with accurate result.

Rational expressions are the complex form of any fraction. So it is clear that this expression have numerator and denominator which are to be solved or convert it into common numerical form by eliminating the common factors from numerator and denominator. But unlike fractions, rational expressions include the various order polynomial functions whose conversion into normal form is also not an easy task, but eventually it has to be done to eliminate the common factors from the polynomial functions. To normalize the polynomials into factors, factorization technique is used which decomposes the single polynomial function into product of its linear factors. After having the rational expression in factor forms, mostly the same factors in numerators and denominator are canceled out, and the remaining equation is the solution of the rational expression.

While simplifying rational expressions, students of class 9th has to remember that the value of polynomial variable must satisfy the following condition which is as:

if F(x) is a function then for any value of x, F(x) should not be equal to zero.

Online solver used for simplifying rational expressions are Factoring calculator and rational expression solver. You can learn the way of implementing solution of online solver for various queries by online math tutor.

 

 

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Rational expression a very important math topic that is some how similar to fractions. So, before moving to rational expressions let’s put some light on fractions. “Fractions are the numbers which are in form of ‘A/B’ where, ‘A’ is numerator and ‘B’ is denominator.

In the rational expressions the numerator and denominator consists of polynomial equations or polynomial terms, these equations consists of number of derivatives of variables. All the operations which can easily apply on fractions can also be apply on rational expressions like addition, subtraction, division, and multiplication. In other words we can say that, “A rational expression is a ratio of two polynomial functions”.

 f(x) = P(x)/Q(x) where, ‘P’ and ‘Q’ are the polynomial functions.

Let’s take an example of rational expression:


x²+y² / x²-y²

In the above example x²+y² is in place of P and x²-y²  in place of ‘Q’.


While Simplifying Rational Expressions we need to factorize numerator and denominator polynomials. After that we need to cancel out all the common terms from the numerator and denominator and we perform the same operation until no common factor left. While solving the rational expression we need to be careful about one more important thing which says that denominator should not be equal to zero, if the denominator is equal to zero then the answer of the question will be infinity. Let’s take an example of rational expression, (x+4) / (x-3)

Here if the value of x is ‘3’ then the result is zero so ‘x’ should not be equal to ‘3’.

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Simplifying rational expression can be really simple

Friends in this session we will talk all about rational expressions, sometimes an rational expression can have fractions of complex form. This complexity is caused because of polynomials functions which are included in numerator and denominator of the rational expression. So the solution of these complex fractions or rational expressions is not so easy it requires an appropriate way.

Lets have some brief discussion on the way of solving any rational expression, while solving complex fraction the first thing is to reduce the polynomials functions of both numerator and denominator to the lowest form

Reducing the polynomials to the lowest form is done by using factorization process for polynomials. After converting polynomial into their factors the common factor is taken out  so that the numerator and denominator is divided by their common factor.

Once all the common factor are eliminated than the value of variables of polynomials function is calculated but one important thing while solving rational expression is that the value of x or variable which is used to form polynomial in denominator can not be such as to make the whole denominator zero.

Let us now explore this way of simplifying rational expressions with example :

normal fraction form is as a/ b, where a is numerator and b is denominator if :

a = x2 – 9

and b = x2 - 16

than find the fraction of x2 – 9/ x2 - 16

the above fraction consist of polynomial functions in its both numerator and denominator which is an rational expression form.

So for solving it first we factorize the polynomial functions:

so a/b = (x + 3) (x -3)/ (x + 4) (x -4)

there is no common factor so the above form is the normalized rational expression.

One thing is clear that the value of x is not be equal to -4 and 4, because if it does then the denominator gets zero and the answer of the expression will be infinity.

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Hey! Friends today we are going to elaborate rational expressions, a simple topic of mathematics. Rational expressions are in the form of complex fractions so we will first talk about fractions in brief. Fractions are in form of P/Q or A/B where, A or P is numerator and Q or B is denominator. Fractions can be represented as ratios, decimal, or percentage. 
Whereas, in rational expressions the numerator and denominator consist of polynomial equations. Polynomial functions or equations consist of number of derivatives of variables it has. All the operations which can be applied on any fraction can also applied on rational expressions like division, multiplication, addition, etc.

While simplifying rational expressions, the first step includes factorization of numerator and denominator polynomials. This factorization process should be repeated by us until we reach the lowest level of polynomial factors. After this, cancel out all the common terms or factors from numerator and denominator. While solving rational expressions, we should be aware of one thing that the numerical value of variable in polynomial is not to be such that the whole polynomial gets zero, because if the denominator polynomial gets zero then expression will give infinity as answer. Let us take a simple example for this:

Suppose a rational expression is given as: (x + 1) / ( x – 2)

Here ‘x’ is variable and if x = 2 than denominator gives zero so ‘x’ should not be equal to ‘2’ for this rational expression.

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Hi friends, before we move on rational expressions lets have a look on fractions. Ya, I know you are aware with fractions, but still I need to give a brief introduction of fractions as rational expressions are related to this only. Fractions are the part of any number in which we have numerator and denominator.  They are in form of a/b or p/q or l/m, etc. where denominator term should not be equal to zero. If this condition is not true then the fraction will result an infinite term. Now, rational expressions are defined as the ratio of two polynomial terms. Polynomial term is the sum of variables and exponent expressions. The operations that are performed on the regular fractions are also performed on rational expressions like addition, subtraction, multiplication, and etc.
Simplification of rational expression is very simple. For simplifying rational expressions, first factor both the terms i.e numerator and denominator completely then reduce the expression by cancelling common factors. Simplifying of radical expression means taking the expression to such a limit from which it can’t reduce to other lower level. The simplification may include the addition, division and other operations. Let’s see how radical expression appears, 4x +3y /   3x +7y, 9x – 8 /9 , etc.
This is only an introduction of rational expression; you can take help of tutorvista. Tutorvista is an online tutoring service which helps kids in learning different subjects. It offers an online solver, using which students can solve all type of math problems. Many other sub solvers are present in online solver such as algebra solver, geometry solver, equation solver and so on. You can learn rational expressions and other math topics in which you are facing any type of problem. To learn mathematics feel free to visit tutorvista, once you take its help you will not move to other sites.

Online Solver simplify radical expressions

Rational expression is one of the most complex and a bit tough topic of mathematics syllabus. Before going in deep lets discuss about rational numbers. Rational number is basically an expression which can be written in the form of fraction like a/b. Here a is the numerator and b is a denominator. The most important thing to remember before simplifying a rational expression is that the denominator in a fraction can never be zero. Let's take an example to understand it better: the numbers 1/3 and -6/1 are rational numbers. A number 2 is also an expression as we can write it as 2/1 = 2 and any number in decimal form can also be written as a rational expression for example: 1.33 is a rational number: 1.33 = 133/100.
There are some theorems which tell us about rational expressions
First one is that any integer is a rational. For example a number n = n/1.
The another theorem is that in the representation of rational number as a fraction is not unique. Like 6/4 = 12/8 = -18/-12.
The third one is that every nonzero rational number or a rational that do not contain a 0 has a representation in lowest term.
Closure Property of Rational Number which tells us how can we multiply, divide and add rational expressions in mathematics.
x/y + a/b = xb + ay / yb and a/b divide c/d = ad/bc.
a/b x c/d = ac/bd.
Sometimes it becomes so difficult to solve rational expressions, as Online Solver is available for free which help us in solving rational problems and also tells us how to arrive an answer. For simplifying rational expressions, we must need to have a good factoring skills. It requires two steps in solving a rational expression. Factor the numerator and denominator is the first step and the second step is divide all common factors that the numerator and denominator have.

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Now I am going to discuss about the Rational Expressions problems. Before proceeding further, let's talk about rational numbers. In simple mathematical manner we can say that a rational number is an expression which can be written as a fraction a/b. Here a is the numerator and b is a denominator. The most important thing to understand is that denominator can never be zero. Let's take an example to understand it better, The fraction 3/5 is rational expression. A number 5 is also a rational expression and we can write it in a form like 5/1.

A number 4.7 is also a number, we can also make it in a rational form : 47/10 further we can make it into mixed fraction.

Closure Property of Rational Number shows as:

x/y + a/b = xb + ay / yb and a/b divide c/d = ad/bc.

a/b x c/d = ac/bd.

For simplifying rational expressions , we must need to have a good factoring skills. It requires two steps in solving rational expressions. The first step is to factor the numerator and denominator. The second step to solve a given rational expression is to divide all common factors that the numerator and denominator have. Dividing a rational number is the most difficult part as it requires key skills. Now we are going to learn how can we divide a rational expression:

12/7 divide by9/14 then we need to take a reciprocal of 9/14 . The reciprocal of 9/14 is 14/9.

Multiply 12/7 with the reciprocal. 12/7 x 14/9 = 24/9 = 8/3 is the required answer.

Rational Expressions in mathematical world

Mathematics is like playing games, students need to practice it regularly to become perfect. So friends today we all are going to learn one of the most important area of mathematical world named as Rational expressions. Before proceeding further, lets discuss about Rational Numbers. Rational number is basically an expression which is written in the form of fractions that is a/b. Here a is the numerator and b is the denominator. The most important thing to remember while solving rational expressions is that denominator can never be zero. For example : 5/2 is a rational expression here 5 is a numerator and 2 is a denominator. The number 7 is also a rational number as it can be written as 7/1. Decimal values are also a rational number for example 2.3 can be written as 23/10.

Some conditions or we can say that theorems which explains about the rational expressions are: First one is that any integer is a rational number. For example a number x = x/1.

Second: the representation of rational number as a fraction is not unique. Like 3/4 = 6/8 = -9/-12.

Third : Every nonzero rational number or a rational that do not contain a 0 has a representation in lowest term.

Closure Property of Rational Number through which addition, multiplications and divisions of rational expressions is done is as follows:

x/y + a/b = xb + ay / yb

a/b divide c/d = ad/bc.

a/b x c/d = ac/bd.

To solve Rational Expressions, students need to house good factoring skills. It requires the following two steps to solve the given rational problem. Factor the numerator and denominator is the first step to solve rational expressions and the second step is divide all common factors that the numerator and denominator have.

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This article is based on rational expressions and how to simplify expressions. Before proceeding further, let’s talk about Rational numbers. In a simple mathematical way we can say that any number that can be expressed as fraction is known as Rational number. For example 2/3 is a rational number, here 2 is the numerator and 3 is a denominator. An essential condition for rational number is that denominator can never be a zero. Decimal number is also a rational number, 1.5 is a rational number that can be expressed as fraction, 1.5 can be written as 15/10 or 3/2.
Expression is a finite combination of symbols that are well formed. A rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials. Here are some examples of rational expressions to understand it better.
6/x-1
It is an equation where 6 is a numerator and x-1 is a denominator. Simplify rational expression means converting complexity into simple and then solving it. In other words, breaking a problem, into simple terms or terminologies can be defined as simplification of rational expressions.Simplify expressions comes with rationalization techniques where we rationalize the denominator. Rationalizing a denominator is the process by which a fraction containing radicals in the denominator is rewritten to have only rational numbers in the denominator.
Sometimes rational expressions come with various algebraic expressions or decimal numbers and with fractions that makes it quite difficult to solve such type of expressions. TutorVista provides Online tutoring services which helps you to solve your mathematics problems and also tells you how to arrive an answer. Online services allows you to take its help any place, where you are able to access internet. TutorVista Online services allows you to solve lessons in Math, worksheets and homework help. It is especially designed to help you to get the desired edge in suceeding the subject.

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Today, I will make you familiar with rational numbers. A rational number is defined as a number that can be written as a simple fraction i.e as a ratio or any number that can be formed by dividing one integer by the other integer. The word rational is derived from the word “ratio”. As the term ratio is used here, lets see what is it? In mathematics, ratio is a relationship between two numbers of the same kind or used to compare two different things. A rational number is expressed as a fraction p/q where, p and q are integers and n ≠ 0. We have algebraic expressions in the same way we have rational expressions, which means that there is a fraction in which the numerator ans/or denominator are polynomials. Let's focus on few examples of rational expressions, 5/ (x-6), (x²– 1)/ (y²+1), etc.

As ratios are related to rational numbers in the same way ratios are also related to proportions. A proportion is a name given to two ratios that are equal. It can be expressed as:

w/x = y/z, here, it is showing two equal fractions

or w:x = y:z, in this we are using colon to represent proportion. When we solve proportions we use to do cross product or cross multiplication.

w:x = y:z is written as w * z = x * y.