Question

Simplify x+2/x^2+2x-3 divide by x+2/x^2-x

Answer 1

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

If
`x\\eq-2`, then we can immediately cancel the factors of
`x+2`:

`\frac{\frac1{x^2+2x-3}}{\frac1{x^2-x}}=(x^2-x)/(x^2+2x-3)`

Factorize the numerator and denominator:

`x^2-x=x(x-1)`

`x^2+2x-3=(x+3)(x-1)`

Next, if
`x\\eq1`, then

`(x^2-x)/(x^2+2x-3)=(x(x-1))/((x+3)(x-1))=\frac x{x+3}`