#### Answer

$\frac{x+34}{(x-1)(x+6)}$

#### Work Step by Step

By inspection, we see that the LCM of the denominators is $(x-1)(x+6)$. Therefore, we create a common denominator using this LCM and obtain:
$\frac{5}{x-1}-\frac{4}{x+6}$
=$\frac{5(x+6)-4(x-1)}{(x-1)(x+6)}$
=$\frac{5x+30-4x+4}{(x-1)(x+6)}$
=$\frac{x+34}{(x-1)(x+6)}$