We need to find a common denominator for the bottom half of the fraction. To do so, we will first factor [tex]x^2-3x-4[/tex].
[tex]x^2-3x-4 = (x+1)(x-4)[/tex]
Notice that both denominators have a x+1 in common. To get the common denominator, we need to multiple the [tex] \frac{5}{x+1} [/tex] by its missing piece, (x-4)
[tex] \frac{5(x-4)}{(x+1)(x-4)} - \frac{x+4}{(x+1)(x-4)} [/tex]
Combine:
[tex] \frac{4(x-6)}{(x+1)(x-4)} [/tex]
When dividing two fractions, we can flip the second one and multiply.
[tex] \frac{1}{3(x+1)(x-1)}[/tex] × [tex] \frac{(x+1)(x-4)}{4(x-6)} [/tex]
There is an (x+1) in the numerator and denominator that cancel.
Answer: [tex] \frac{x-4}{12(x-1)(x-6)} [/tex]
