How do you solve $\frac{2}{x + 6} = \frac{9}{8} - \frac{4}{x + 6}$ $2/(x +6) = 9/8 - 4/(x+6)$ ?

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How do you solve $\frac{2}{x + 6} = \frac{9}{8} - \frac{4}{x + 6}$ $2/(x +6) = 9/8 - 4/(x+6)$ ?

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Answer 1 · 2016-01-02T01:31:43

$x = - \frac{2}{3}$ $x=-2/3$

Explanation:

Original solution
Place on a common denominator and solve the resulting linear equation.
$\frac{16}{8 x + 48}$ $16/(8x + 48)$ = $\frac{9 x + 54}{8 x + 48}$ $(9x + 54)/ (8x + 48)$ - $\frac{32}{8 x + 48}$ $32/(8x + 48)$

16 - 54 + 32 = 9x

-6 = 9x

$- \frac{2}{3}$ $-2/3$ = x

Simplier solution
$\frac{2}{x + 6} = \frac{9}{8} - \frac{4}{x + 6}$ $2/(x+6)=9/8-4/(x+6)$
$\frac{2}{x + 6} + \frac{4}{x + 6} = \frac{9}{8}$ $2/(x+6)+4/(x+6)=9/8$
$\frac{6}{x + 6} = \frac{9}{8}$ $6/(x+6)=9/8$
Multiply both sides by $(x + 6)$ $(x+6)$ and divide by $\frac{9}{8}$ $9/8$
$6 \cdot \frac{8}{9} = x + 6$ $6*8/9=x+6$
$x = \frac{2 \cdot 8}{3} - 6 = \frac{16}{3} - 6 = 5 \frac{1}{3} - 6 = - \frac{2}{3}$ $x=(2*8)/3-6=16/3-6=5 1/3-6=-2/3$
The solution is $- \frac{2}{3}$ $-2/3$ .

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How do you solve $\frac{2}{x + 6} = \frac{9}{8} - \frac{4}{x + 6}$ $2/(x +6) = 9/8 - 4/(x+6)$ ?

1 Answer

Explanation:

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How do you solve $\frac{2}{x + 6} = \frac{9}{8} - \frac{4}{x + 6}$ $2/(x +6) = 9/8 - 4/(x+6)$ ?