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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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.