$\frac{x}{y} \div \frac{a}{b} \implies \frac{x}{y} \times \frac{b}{a}$

$\large \frac{x^2 + 2x -3}{x^2+x-2} \div \frac{x^2 + x - 6}{x^2-4}$

Factorising all expressions we get:

$\large \frac{(x+3)(x-1)}{(x+2)(x-1)} \div \frac{(x+3)(x-2)}{(x+2)(x-2)}$

Cancelling the like factors:

$\large \frac{x+3}{x+2} \div \frac{x+3}{x+2}$

Flipping the sign and right fractions:

$\large \frac{x+3}{x+2} \cdot \frac{x+2}{x+3}$

Cancelling like factors gives us $\boxed{1}$ which is the answer.

Well... $x$ wasn't given, so I guessed that all the terms would cancel. Since the answer machine only accept numbers, it wouldn't be answers like infinity or undefined. It wouldn't be 0, because it's multiplication, so the answer is $\boxed{1}$ .