How do you solve -2/(x-1)=(x-8)/(x+1)?

1 Answer
Jun 20, 2017

The answer is x = 2, 5.

Explanation:

We see that the equation is a proportion, so we can cross-multiply to start off. Cross-multiplying, the equation becomes:

-2(x+1) = (x-1)(x-8)

We can then distribute the -2 on the left side, while multiplying out the right-hand side using FOIL (or any method you learned).

-2x - 2 = x^2 - 9x + 8

Adding 2x and 2 to both sides gives us

0 = x^2 - 7x + 10

Now, we can factor the equation to get the zeroes of the equation or the values for x. We see that -5*-2 = 10 (the third term in the expansion) and -5+(-2)=-7 (the second term in the expansion), so those should be the second terms in each binomial. This is just one method of factoring; there are many other ways you could use. After factoring, we get:

0 = (x - 5)(x - 2)

To get the zeroes, we see that if x-5 = 0, then x=5, and if x-2 = 0, then x=2.

Therefore, x = 2, 5.