Simplify Rational Expressions

This example is about simplifying rational expressions.

Example 1


For $x \neq 2$, $\dfrac{x^2+x-6}{x-2} = $

  1. $x-2$

  2. $x-3$

  3. $x+3$

  4. $x$

  5. $x+2$

Solution



This example is about simplifying rational expressions.
  1. The 5 possible solutions indicate that we need to simplify the given rational expression. But in order to simplify the given expression, we need to factor the numerator. In order to simplify the $x-2$ in the denominator one of the factors of the numerator must be $x- 2$. Hence

    $\dfrac{x^2+x-6}{(x-2)} = \dfrac{(x-2)(x+3)}{(x-2)}$

    We now simplify

    $= \dfrac{\colorcancel{red}{(x-2)}(x+3)}{\colorcancel{red}{(x-2)}}$

    $=x+3$

    Answer C

privacy policy

{ezoic-ad-1}

{ez_footer_ads}