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

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:

$- 2 \left(x + 1\right) = \left(x - 1\right) \left(x - 8\right)$

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

$- 2 x - 2 = {x}^{2} - 9 x + 8$

Adding $2 x$ and $2$ to both sides gives us

$0 = {x}^{2} - 7 x + 10$

Now, we can factor the equation to get the zeroes of the equation or the values for $x$. We see that $- 5 \cdot - 2 = 10$ (the third term in the expansion) and $- 5 + \left(- 2\right) = - 7$ (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:

$0 = \left(x - 5\right) \left(x - 2\right)$

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

Therefore, $x = 2 , 5$.