# How do you solve 12/21= (x-5)/x?

Mar 10, 2016

$x = \frac{105}{9} \mathmr{and} 11 \frac{6}{9} \mathmr{and} 11 \frac{2}{3}$

#### Explanation:

$\frac{12}{21} = \frac{x - 5}{x}$

Cross multiply to eliminate the denominators.
$12 \left(x\right) = \left(x - 5\right) 21$

Use distributive property to eliminate the ( ).
$12 x = 21 x - 105$

Combine like terms.
$12 x - 21 x = \cancel{21 x} - \cancel{21 x} - 105$

$- 9 x = - 105$

Divide by the coefficient to isolate the variable.
$\frac{\cancel{- 9} x}{\cancel{- 9}} = - \frac{105}{-} 9$

$x = \frac{105}{9} \mathmr{and} 11 \frac{6}{9} \mathmr{and} 11 \frac{2}{3}$