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.

 

 

Online Solver solves Rational Expression Problems

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.

Students can take help of online solver provided by TutorVista to learn more about rational expression.

Tutorvista helps students in learning rational expressions

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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Solve Rational Expressions with online help

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.
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