Question

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

Answer 1

we are given

`((x^2+x-6))/((x^2-4))*((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

=
`((x+3)(x-2))/((x-2)(x+2))*((x-3)(x+3))/((x+3)^2)`

step-2: Cancel common terms

we get

=
`((x+3))/((x+2))*((x-3))/((x+3))`

we can again cancel numerator and denominator

and we get

=
`((x-3))/((x+2))`.............Answer