# Rational Expressions

Rational expressions is defined as the quotient p(x)/q(x) of two polynomials p(x) and q(x) where q(x) is non zero polynomial.

for example if p(x)=x^{2}-2x and q(x)=2x-4 (non zero polynomial) are two polynomials then quotient p(x)/q(x)=x^{2}-2x/2x-4 is known as rational expression of polynomials.where p(x) is known as numerator and q(x) is known as denominator of rational expression.

**Example of rational expression**

- p(x)/q(x)=(x
^{3}-2x)/(8x-4) - p(x)/q(x)=(x
^{3}-2x^{2})/(2x^{2}-4) - p(x)/q(x)=(x
^{2}-x+3)/(x-5) - p(x)/q(x)=(x
^{3}-2x^{2}-3)/(x^{2}-2)

## Equality of rational expressions

Two Rational expressions are always equal if numerator of 1st expression * denominator of 2nd expression is equal to denominator of 1st expression * numerator of 2nd expression.

For example if you have two rational expression p(x)/q(x) and m(x)/n(x) then that rational expression are said to be equal if p(x)n(x)=q(x)m(x).

### Addition of rational expressions

Sum of two rational expressions is defined as (p(x)n(x)+m(x)q(x))/(n(x)q(x)) where rational expressions of polynomials are p(x)/q(x) and m(x)/n(x).
** Example**

first rational expressions is x+4/x-8 and second rational expressions is x^{2}+3/x-1 then addition of rational expressions are

Sum of two rational expressions is ((x+4)*(x-1)+ (x^{2}+3)*(x-8))/(x-8)(x-1)