How do you solve the rational equation $\frac{7}{x - 4} = 1 + \frac{9}{x + 4}$ $7/(x-4) = 1 + 9/(x+4)$ ?

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How do you solve the rational equation $\frac{7}{x - 4} = 1 + \frac{9}{x + 4}$ $7/(x-4) = 1 + 9/(x+4)$ ?

1 Answer

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Answer 1 · 2016-03-03T18:14:13

$7 (x + 4) = 1 (x - 4) (x + 4) + 9 (x - 4) \to 7 x + 28 = x^{2} - 16 + 9 x - 36 \to 0 = x^{2} + 2 x - 80 \to 0 = (x + 10) (x - 8) \to x = - 10 or x = 8$ $7(x+4)=1(x-4)(x+4)+9(x-4) ->7x+28=x^2-16+9x-36 ->0=x^2+2x-80 ->0=(x+10)(x-8) -> x=-10 or x=8$

Explanation:

First, multiply everything on both sides by the common denominator and simplify. Then put everything on one side and solve for x.

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How do you solve the rational equation $\frac{7}{x - 4} = 1 + \frac{9}{x + 4}$ $7/(x-4) = 1 + 9/(x+4)$ ?

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How do you solve the rational equation $\frac{7}{x - 4} = 1 + \frac{9}{x + 4}$ $7/(x-4) = 1 + 9/(x+4)$ ?