How would I solve X/X+2 - 6/X-1 = 4 whilst using the quadratic formula?

Question

During my first attempt I simplified the left hand side into a single fraction and I got X^2 -7X -12 / (X-1)(X+2)

But what should I do next?

Answer 1

You are on the right track! The oooooooother side needs to also go over the same denominator. You can't simplify just the one side.

Since the common denominator is (x + 2)(x - 1), the other side looks like...

4x² + 4x - 8/(x - 1)(x + 2)

Now, once you have the common denominator, you don't need it anymore. We only deal with the numerators.

x2 - 7x - 12 = 4x² + 4x - 8

3x² + 11x + 4 = 0

Now, you have a = 3, b = 11 and c = 4 for your quadratic formula.

Go!