Question

How do you multiply and simplify `\frac { 1} { x - 4} \cdot \frac { x ^ { 2} + 2x - 24} { x - 5}`?

Answer 1

`(x+6)/(x-5)`

Explanation:

`x^2+2x-24 = (x+6)(x-4)`

`1/(x-4) * (x^2+2x-24)/(x-5) = 1/(x-4) * ((x+6)(x-4))/(x-5)`

`1/(x-4) * ((x+6)(x-4))/(x-5) = 1/cancel(x-4) * ((x+6)cancel((x-4)))/(x-5)`

`=1*(x+6)/(x-5)`

`=(x+6)/(x-5)`