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

1 Answer
Sep 17, 2015

(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)