# Math's: Special Products: Rational Expressions: Meaning and Mathematical Operations

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## Rational Expressions: Meaning

An algebraic expression, which can be expressed in the form of , where and are polynomials, is called a rational expression.

Examples-

1. Which of the following algebraic expressions are rational expressions?

(i) (ii) (iii) (iv) (v) (vi)

Solution: (i) is a polynomial since both and are polynomials.

(ii) is a rational expression since is a polynomial of degree zero and is also a polynomial.

(iii) is not a rational expression because is not a polynomial (the power of variable not being a whole number) although is a polynomial.

(iv) is a rational expression since both the numerator and denominator are polynomials.

(v) can be expressed as where both and are polynomials. So, is a rational expression.

(v) In the expression, both the numerator and the denominator are not polynomials because in , the variable occurs in denominator and in , the variable has fractional power. So, the expression is not a rational expression.

## Mathematical Operations on Rational Expressions

The four basic mathematical operations (addition, subtraction, multiplication and division) on rational expressions are performed in the same manner as in the case of rational numbers.

## Addition and Subtraction of Rational Expressions

• Step 1- Take the LCM of denominators of rational expressions.

• Step 2- Make the denominators of the rational expressions equal to the LCM

• Step 3- Add or Subtract the numerators and write the LCM in the denominator

Example- -

Sol- LCM-

## Multiplication and Division of Rational Expressions

Product of two rational expressions is the expression obtained by multiplying the numerators and denominators of the expressions with each other i.e. . Similarly, division of rational expressions is done by the division of the numerators and denominators of the expressions i.e. .

Example-(i)

Sol-

Example (ii)

Sol-

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