\(\frac{x^2+x-6}{x^2-7x+10}\)
When you factor a quadratic ax² + bx + c, it becomes (x+m)(x+n), where mn = ac, and m+n = b.
In x²+x-6, we want to find two numbers that multiply to -6 and add to 1.
3 and -2 satisfy both of these criteria, so there are our factors.
\(\frac{(x+3)(x-2)}{x^2-7x+10}\)
In x²-7x+10, we want to find two numbers that multiply to 10 and add to -7.
-5 and -2 satisfy both of these criteria, so there are our factors.
\(\frac{(x+3)(x-2)}{(x-5)(x-2)}\)
The (x-2) cancels and we're left with
\(\boxed{\frac{x+3}{x-5}}\)
