# How do you solve (12x-5) / (6x+3) = 2 - 5/x?

Sep 7, 2017

$x = - \frac{15}{19}$

#### Explanation:

NOTE: There's more than one way to skin a cat.

$\frac{12 x - 5}{6 x + 3} = 2 - \frac{5}{x}$

Step 1: multilply both sides by $x$

$x \cdot \left(\frac{12 x - 5}{6 x + 3}\right) = \left(2 - \frac{5}{x}\right) \cdot x$

$\frac{12 {x}^{2} - 5 x}{6 x + 3} = 2 x - 5$

Step 2: multiply both sides by $\left(6 x + 3\right)$

$6 x + 3 \cdot \left(\frac{12 {x}^{2} - 5 x}{6 x + 3}\right) = \left(2 x - 5\right) \cdot \left(6 x + 3\right)$

$12 {x}^{2} - 5 x = 12 {x}^{2} + 6 x - 30 x - 15$

Step 3: simplify

$- 5 x = - 24 x - 15$

$19 x = - 15$

$x = - \frac{15}{19}$

Step 4: check your answer for $x$

$\frac{12 x - 5}{6 x + 3} = 2 - \frac{5}{x}$

$\frac{12 \cdot \left(- \frac{15}{19}\right) - 5}{6 \cdot \left(- \frac{15}{19}\right) + 3} = 2 - \frac{5}{- \frac{15}{19}}$

$\frac{\left(- \frac{180}{19}\right) - \left(\frac{95}{19}\right)}{\left(- \frac{90}{19}\right) + \left(\frac{57}{19}\right)} = 2 + 5 \cdot \left(\frac{19}{15}\right)$

$\frac{- 180 - 95}{- 90 + 57} = 2 + \frac{19}{3}$

$\frac{- 180 - 95}{- 90 + 57} = \frac{6}{3} + \frac{19}{3}$

$\frac{275}{33} = \frac{25}{3}$

$11$ goes into $275$ $25$ times and $11$ goes into $33$ $3$ times

$\frac{25}{3} = \frac{25}{3}$