Question

How do you simplify `(2a^2-a-6 )/(2a^2+7a+6)*(a^2-2a-8)/(a^2+a-6)`?

Answer 1

`(a-4)/(a+3)`

Explanation:

`(2a^2-a-6)/(2a^2+7a+6) * (a^2-2a-8)/(a^2+a-6)=`

`=(2a^2-4a+3a-6)/(2a^2+4a+3a+6)*(a^2-4a+2a-8)/(a^2-2a+3a-6)=`

`=(2a(a-2)+3(a-2))/(2a(a+2)+3(a+2))*(a(a-4)+2(a-4))/(a(a-2)+3(a-2))=`

`=((2a+3)(a-2))/((2a+3)(a+2))*((a+2)(a-4))/((a+3)(a-2))=(a-4)/(a+3)`