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

Jul 9, 2016

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

Explanation:

$\frac{10}{3 x} - 8 = \frac{2}{x}$ Multiply both sides by $x$
$\frac{10 x}{3 x} - 8 x = 2$
$\frac{10 \cancel{x}}{3 \cancel{x}} - 8 x = 2$ Multiply both sides by $3$
$\frac{10 \times 3}{3} - \left(\left(8 x\right) \times 3\right) = 2 \times 3$
$\frac{10 \times \cancel{3}}{\cancel{3}} - 24 x = 6$
$10 - 24 x = 6$
$- 24 x = 6 - 10 = - 4$
$x = \frac{- 4}{- 24} = \frac{1}{6}$