((x^2+13x+40)/(x^2+2x-35))*((x^2-4x-5)/(x^2+6x-16))

Question

Multiply the equation and simplify

Answer 1

x²+13x+40=(x+5)(x+8);

x²+2x-35=(x-5)(x+7);

x²-4x-5=(x-5)(x+1);

x²+6x-16=(x+8)(x-2).

Product becomes:

{(x+5)(x+8)/[(x-5)(x+7)]}{(x-5)(x+1)/[(x+8)(x-2)]}=

(x+5)(x+1)/[(x+7)(x-2)]=(x²+6x+5)/(x²+5x-14).

This can be further reduced:

(x²+5x-14+x+19)/(x²+5x-14)=1+[(x+19)/(x²+5x-14)].