Chapter 8.3, Problem 14MCQ

To determine

To simplify: the expression

Answer to Problem 14MCQ

The value of the expression $\frac{x-4}{x^2-3x-4}+\frac{x+1}{2x-8}$ is $\frac{2\left(x-4\right)+{\left(x+1\right)}^2}{2\left(x-4\right)+\left(x+1\right)}$

Explanation of Solution

Given information: The expression is $\frac{x-4}{x^2-3x-4}+\frac{x+1}{2x-8}$

Calculation:

From the expression $\frac{x-4}{x^2-3x-4}+\frac{x+1}{2x-8}$

Take LCM of the both denominator

LCM $=2\left(x-4\right)\left(x+1\right)$

  $\begin{array}{l}\frac{x-4}{x^2-3x-4}+\frac{x+1}{2x-8}\\ \frac{2\left(x-4\right)}{2\left(x-4\right)\left(x+1\right)}+\frac{\left(x+1\right)\left(x+1\right)}{2\left(x-4\right)\left(x+1\right)}\\ \frac{2\left(x-4\right)+{\left(x+1\right)}^2}{2\left(x-4\right)+\left(x+1\right)}\end{array}$