# How do you solve 3/(4x)-1/2=2/(3x)-2 and check for extraneous solutions?

Aug 15, 2016

$x = - \frac{1}{18}$

#### Explanation:

$\frac{3}{4 x} - \frac{1}{2} = \frac{2}{3 x} - 2 \text{ } x \ne 0$

The biggest problem is the fractions. Multiply by the LCM to cancel the denominators. LCM = $12 x$

$\frac{\textcolor{red}{12 x \times} 3}{4 x} - \frac{\textcolor{red}{12 x \times} 1}{2} = \frac{\textcolor{red}{12 x \times} 2}{3 x} - \left(\textcolor{red}{12 x \times} 2\right)$

$\frac{\textcolor{red}{{\cancel{12 x}}^{3} \times} 3}{\cancel{4 x}} - \frac{\textcolor{red}{{\cancel{12}}^{6} x \times} 1}{\cancel{2}} = \frac{\textcolor{red}{{\cancel{12 x}}^{4} \times} 2}{\cancel{3 x}} - \left(\textcolor{red}{12 x \times} 2\right)$

$9 - 6 x = 8 - 24 x$

$24 x - 6 x = 8 - 9$

$18 x = - 1$

$x = - \frac{1}{18}$