Question

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

Answer 1

`(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.


`((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.


`((x+3)(x-2))/((x-5)(x-2))`

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


`\boxed{(x+3)/(x-5)}`