Chapter A.5, Problem 26AYU

To determine

To find: Simplify the given in factored form.

Answer to Problem 26AYU

$\frac{x^2+7x-1}{\left(x+8\right)\left(x-3\right)}$

Explanation of Solution

Given:

$\frac{x}{x-3}-\frac{x+1}{x^2+5x-24}$

Calculation:

$\frac{x}{x-3}-\frac{x+1}{x^2+5x-24}=\frac{x}{x-3}-\frac{x+1}{\left(x+8\right)\left(x-3\right)}$

$=\frac{x\left(x+8\right)-x+1}{\left(x+8\right)\left(x-3\right)}$

$=\frac{x^2+7x-1}{\left(x+8\right)\left(x-3\right)}$