# How do you solve (x-2)/x<(x-4)/(x-6)?

Oct 10, 2016

The solution of the inequality is $x < 3$.

#### Explanation:

This inequality is solved by first cross multiplying, then solving the inequality.

$\frac{x - 2}{x} < \frac{x - 4}{x - 6}$
$\left(x - 2\right) \left(x - 6\right) < x \left(x - 4\right)$
${x}^{2} - 6 x - 2 x + 12 < {x}^{2} - 4 x$
${x}^{2} - 8 x + 12 < {x}^{2} - 4 x$
${x}^{2} - {x}^{2} - 8 x + 12 < {x}^{2} - {x}^{2} - 4 x$
$- 8 x + 12 < - 4 x$
$- 8 x + 4 x + 12 < - 4 x + 4 x$
$- 4 x + 12 < 0$
$- 4 x + 12 - 12 < 0 - 12$
$- 4 x < - 12$
$\frac{- 4 x}{-} 4 < \frac{- 12}{-} 4$
$x < 3$