Question

How do you multiply and simplify `\frac { x ^ { 2} - 3x - 10} { x ^ { 2} - 4x - 12} \cdot \frac { 6- x } { x ^ { 2} - 25}`?

Answer 1

`-1/(x+5)`

Explanation:

First we factorise everything:
`((x+2)(x-5))/((x+2)(x-6))*(6-x)/((x-5)(x+5))=((x+2)(x-5)(6-x))/((x+2)(x-6)(x-5)(x+5))`

`(cancel((x+2))cancel((x-5))(6-x))/(cancel((x+2))(x-6)cancel((x-5))(x+5))=(6-x)/((x-6)(x+5))`

`(6-x)=-(x-6)`

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