X^2 + x - 6 over x^2 - 7x + 10
simplify fully

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.



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.



The (x-2) cancels and we're left with