# How do you solve for x in (5a)/x = (5b)/(x-1)?

Feb 26, 2016

First, simplify by the property $\frac{a}{b} = \frac{m}{n} \to a \times n = b \times m$

#### Explanation:

$5 b x = \left(x - 1\right) 5 a$

$5 b x = 5 a x - 5 a$

$5 b x - 5 a x = - 5 a$

$5 x \left(b - a\right) = - 5 a$

$5 x = \frac{- 5 a}{b - a}$

$x = - \frac{\frac{5 a}{b - a}}{5}$

$x = - \frac{5 a}{5 \left(b - a\right)}$

$x = - \frac{5 a}{5 b - 5 a}$

Practice exercises:

1. Solve for x. Hint for b): place on an equivalent denominator.

a) $\frac{1 + 5 a}{2 x} = \frac{3 z - 4 x}{5 a}$

b). $\frac{1}{2 x} + \frac{1}{y z} = \frac{3}{x z y}$

Good luck!