Question

How do you multiply and simplify `\frac { 12x + 48} { 6x - 15} \cdot \frac { 4x ^ { 2} - 25} { x ^ { 2} + 9x + 20}`?

Answer 1

`=(4(2x+5))/((x+5))`

Explanation:

In order to be able to cancel, you need to factorise as far as possible.

`(12x+48)/(6x-15) xx (4x^2 -25)/(x^2 +9x+20)`

`=(12(x+4))/(3(2x-5)) xx ((2x-5)(2x+5))/((x+4)(x+5))`

Now cancel like factors:

`(=cancel12^4cancel((x+4)))/(cancel3cancel((2x-5))) xx (cancel((2x-5))(2x+5))/(cancel((x+4))(x+5))`

`=(4(2x+5))/((x+5))`