To solve the multiplication, we should first factorize each quadratic polynomial. Hence,
x^2-x-6=x^2-3x+2x-6=x(x-3)+2(x-3)=(x+2)(x-3)x2−x−6=x2−3x+2x−6=x(x−3)+2(x−3)=(x+2)(x−3)
x^2+4x+3=x^2+3x+x+3=x(x+3)+1(x+3)=(x+1)(x+3)x2+4x+3=x2+3x+x+3=x(x+3)+1(x+3)=(x+1)(x+3)
x^2-x-12=x^2-4x+3x-12=x(x-4)+3(x-4)=(x+3)(x-4)x2−x−12=x2−4x+3x−12=x(x−4)+3(x−4)=(x+3)(x−4)
x^2-x-8=x^2-4x+2x-8=x(x-4)+2(x-4)=(x+2)(x-4)x2−x−8=x2−4x+2x−8=x(x−4)+2(x−4)=(x+2)(x−4)
Hence (x^2-x-6)/(x^2+4x+3)*(x^2-x-12)/(x^2-x-8)x2−x−6x2+4x+3⋅x2−x−12x2−x−8
= ((x+2)(x-3))/((x+1)(x+3))*((x+3)(x-4))/((x+2)(x-4))(x+2)(x−3)(x+1)(x+3)⋅(x+3)(x−4)(x+2)(x−4)
= ((cancel(x+2))(x-3))/((x+1)(cancel(x+3)))*((cancel(x+3))(cancel(x-4)))/(cancel((x+2))(cancel(x-4)))
=(x-3)/(x+1)
