Q. 7.3 - Intermediate Algebra

Question

Simplify:$\frac{x^2-x-2}{x^2-3x+2}$

Step-by-Step Solution

Answer

The simplest form of the given rational expression is$\frac{(x+1)}{\left(x-1\right)}.$

Step 1 . Given information

The given rational expression is$\frac{x^2-x-2}{x^2-3x+2}$

Step 2 .   Simplify

$$\begin{gathered} \frac{x^2-x-2}{x^2-3x+2}=\frac{\left(x-2\right)(x+1)}{\left(x-2\right)\left(x-1\right)} \text{Factorize numerator and denominator } \\ =\frac{(x+1)}{\left(x-1\right)} \text{Cancel common factors of }\mathrm{numerator} \mathrm{and} \mathrm{denominator} \end{gathered}$$