How do you solve $\frac{10}{3 x} - 8 = \frac{2}{x}$ $10/(3x)-8=2/x$ and find any extraneous solutions?

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How do you solve $\frac{10}{3 x} - 8 = \frac{2}{x}$ $10/(3x)-8=2/x$ and find any extraneous solutions?

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Answer 1 · 2016-07-09T03:24:07

$x = \frac{1}{6}$ $x=1/6$

Explanation:

$\frac{10}{3 x} - 8 = \frac{2}{x}$ $10/(3x)-8=2/x$ Multiply both sides by $x$ $x$
$\frac{10 x}{3 x} - 8 x = 2$ $(10x)/(3x)-8x=2$
$(10 cancelx)/(3 cancelx)-8x=2$ Multiply both sides by $3$
$(10xx3)/3-((8x)xx3)=2xx3$
$(10xxcancel3)/cancel3-24x=6$
$10-24x=6$
$-24x=6-10=-4$
$x=(-4)/(-24)=1/6$

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How do you solve $\frac{10}{3 x} - 8 = \frac{2}{x}$ $10/(3x)-8=2/x$ and find any extraneous solutions?

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How do you solve $\frac{10}{3 x} - 8 = \frac{2}{x}$ $10/(3x)-8=2/x$ and find any extraneous solutions?