# How do you solve (3x-1)/3-(x-3)/15=(2x+3)/2?

Apr 19, 2018

Isolate the first part:

$\frac{3 x - 1}{3} - \frac{x - 3}{15}$

Get the denominator (both bottom numbers) equal buy multiplying the tops and bottoms. 15 is a common multiple of 3 and 15 so multiply the first fraction by 5 and the second by 1.

$\frac{5 \left(3 x - 1\right)}{15} - \frac{x - 3}{15}$ Now expand and subtract the two

$\frac{15 x - 5}{15} - \frac{x - 3}{15}$

$\frac{15 x - 5 - x + 3}{15} = \frac{14 x - 2}{15}$

Put it back in the whole equation:

$\frac{14 x - 2}{15} = \frac{2 x + 3}{2}$

Both have a common multiple of 30, so, multiply the first part by 2 and the second by 15.

$\frac{2 \left(14 x - 2\right)}{30} = \frac{15 \left(2 x + 3\right)}{30}$

$\frac{28 x - 4}{30} = \frac{30 x + 45}{30}$

$28 x - 4 = 30 x + 45$
$- 2 x = 49$

$x = - 24.5$