Question

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

Answer 1

$\dfrac{\frac{x+2}{x^2+2x-3}}{\frac{x+2}{x^2-x}}$

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

$\dfrac{\frac1{x^2+2x-3}}{\frac1{x^2-x}}=\dfrac{x^2-x}{x^2+2x-3}$

Factorize the numerator and denominator:

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

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

Next, if $x\neq1$, then

$\dfrac{x^2-x}{x^2+2x-3}=\dfrac{x(x-1)}{(x+3)(x-1)}=\dfrac x{x+3}$