How do you solve $- \frac{2}{x - 1} = \frac{x - 8}{x + 1}$ $-2/(x-1)=(x-8)/(x+1)$ ?

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How do you solve $- \frac{2}{x - 1} = \frac{x - 8}{x + 1}$ $-2/(x-1)=(x-8)/(x+1)$ ?

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Answer 1 · 2017-06-20T23:33:37

The answer is $x = 2, 5$ $x = 2, 5$ .

Explanation:

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

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

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

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

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

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

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

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

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

Therefore, $x = 2, 5$ $x = 2, 5$ .

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How do you solve $- \frac{2}{x - 1} = \frac{x - 8}{x + 1}$ $-2/(x-1)=(x-8)/(x+1)$ ?

1 Answer

Explanation:

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