Question

How do you simplify `(x^2 - 16 )/( 2x^2 - 9x + 4) div (2x^2 + 14x + 24) /( 4x + 4)`?

Answer 1

`(2(x+1))/((2x-1)(x+3))`

Explanation:

By factoring note that:

`(x^2-16)/(2x^2-9x+4)÷(2x^2+14x+24)/(4x+4)=`

`((x+4)(x-4))/((2x-1)(x-4))*(4(x+1))/(2(x+3)(x+4))`

Cancel like terms:

`(cancel((x+4))cancel((x-4)))/((2x-1)cancel((x-4)))*(cancel(4)color(blue)(2)(x+1))/(cancel(2) (x+3)cancel((x+4)))=`

`(2(x+1))/((2x-1)(x+3))`