Question

Simplify the expression. x2 + x - 6 /x2 - 4 · x2 - 9/ x2 + 6x + 9

Answer 1

we are given

$\frac{(x^2+x-6)}{(x^2-4)}*\frac{(x^2-9)}{(x^2+6x+9)}$

step-1: Factor terms

$x^2+x-6=(x+3)(x-2)$

$x^2+6x+9=(x+3)^2$

$x^2-4=(x-2)(x+2)$

now, we can plug these values

and we get

=$\frac{(x+3)(x-2)}{(x-2)(x+2)}*\frac{(x-3)(x+3)}{(x+3)^2}$

step-2: Cancel common terms

we get

=$\frac{(x+3)}{(x+2)}*\frac{(x-3)}{(x+3)}$

we can again cancel numerator and denominator

and we get

=$\frac{(x-3)}{(x+2)}$.............Answer