Question

how do you simplify rational expressions?​

Answer 1

The simplification of rational expressions is explained

Solution:

Rational expressions are fractions that have a polynomial in the numerator, denominator, or both.

Rational expressions contain variables, they can be simplified in the same way that numerical fractions are simplified.

Steps to simplify rational expressions:

Let us see it with an example:

$\frac{3 x^{2}-3 x}{3 x^{3}-6 x^{2}+3 x}$

1) Look for factors that are common to the numerator & denominator

$\frac{3 x(x-1)}{3 x\left(x^{2}-2 x+1\right)}$

2) 3x is a common factor to the numerator & denominator. Note that it is clear that x ≠0

3) Cancel the common factor

$\frac{x-1}{x^{2}-2 x+1}$

4) If possible, look for other factors that are common to the numerator and denominator

$\frac{x-1}{(x-1)(x-1)}$

5) After cancelling, you are left with $\frac{1}{(x-1)}$

6) The final simplified rational expression is valid for all values of "x" except 0 and 1

We have to follow the same procedure for any rational expression.