Question

Simplify the complex fraction

Answer 1

We need to find a common denominator for the bottom half of the fraction. To do so, we will first factor $x^2-3x-4$.

$x^2-3x-4 = (x+1)(x-4)$

Notice that both denominators have a x+1 in common. To get the common denominator, we need to multiple the $\frac{5}{x+1}$ by its missing piece, (x-4)

$\frac{5(x-4)}{(x+1)(x-4)} - \frac{x+4}{(x+1)(x-4)}$

Combine:

$\frac{4(x-6)}{(x+1)(x-4)}$

When dividing two fractions, we can flip the second one and multiply.

$\frac{1}{3(x+1)(x-1)}$ × $\frac{(x+1)(x-4)}{4(x-6)}$

There is an (x+1) in the numerator and denominator that cancel.

Answer: $\frac{x-4}{12(x-1)(x-6)}$