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
`(5)/(x+1)` by its missing piece, (x-4)


`(5(x-4))/((x+1)(x-4)) - (x+4)/((x+1)(x-4))`

Combine:


`(4(x-6))/((x+1)(x-4))`

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


`(1)/(3(x+1)(x-1))` ×
`((x+1)(x-4))/(4(x-6))`

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

Answer:
`(x-4)/(12(x-1)(x-6))`