# How do you solve 3/2 - 1/(x-5) = -2/(2x - 10)?

Oct 7, 2015

I found no solution! The equation is not true.

#### Explanation:

We can write it as:
$\frac{3}{2} - \frac{1}{x - 5} = - \frac{2}{2 \left(x - 5\right)}$
$\frac{3 \left(x - 5\right) - 2}{\cancel{\left(2 \left(x - 5\right)\right)}} = - \frac{2}{\cancel{\left(2 \left(x - 5\right)\right)}}$
$3 x - 15 - 2 = - 2$
$3 x = 15$
$x = \frac{15}{3} = 5$
BUT
$x = 5$ makes both denominators equal to zero!