Question

How do you simplify `(3x^2+14x+8)/ (2x^2+7x-4) * (2x^2+9x-5)/(3x^2+16x+5)`?

Answer 1

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

Explanation:

Factor the terms:

`(3x^2+14x+8)/(2x^2+7x-4)*(2x^2+9x-5)/(3x^2+16x+5)=`

`((3x+2)(x+4))/((2x-1)(x+4))*((2x-1)(x+5))/((3x+1)(x+5))`

Cancel the identical terms found in the factorisation:

`((3x+2)(x+4))/((2x-1)(x+4))*((2x-1)(x+5))/((3x+1)(x+5))=`

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