Question

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

Answer 1

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`.