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

May 9, 2015

Given:
$\frac{x}{10} - \frac{1}{2} = - \frac{3}{5 x}$

to make the denominator of the L.H.S equal we take the L.C.M:

L.C.M of 10 and 2 $=$ 10

$\left(\frac{x}{10}\right) - \frac{1 \times 5}{2 \times 5} = - \frac{3}{5 x}$
$\left(\frac{x}{10}\right) - \frac{5}{10} = - \frac{3}{5 x}$

$\frac{x - 5}{10} = - \frac{3}{5 x}$
on cross multiplying:

$\left(x - 5\right) \times \left(5 x\right) = - 3 \times 10$

$5 {x}^{2} - 25 x = - 30$

$5 {x}^{2} - 25 x + 30 = 0$

dividing the equation by 5:
${x}^{2} - 5 x + 6 = 0$

solving this equation by grouping / splitting the middle term:

${x}^{2} - 2 x - 3 x + 6 = 0$ ($2 \times 3 = 6 \mathmr{and} 2 + 3 = 5$)

$= x \left(x - 2\right) - 3 \left(x - 2\right)$

$= \left(x - 2\right) \left(x - 3\right)$

$x$ has two values here:
$x = 2 \mathmr{and} x = 3$