# How do you solve 10/x - 12/(x-3) + 4 = 0?

Feb 12, 2016

You must put on a common denominator.

#### Explanation:

The LCD (Least Common Denominator) is $x \left(x - 3\right)$

$\frac{10 \left(x - 3\right)}{x \left(x - 3\right)} - \frac{12 \left(x\right)}{x \left(x - 3\right)} + \frac{4 \left({x}^{2} - 3 x\right)}{x \times x - 3} = 0$

We can now eliminate the denominators:

$10 x - 30 - 12 x + 4 {x}^{2} - 12 x = 0$

$4 {x}^{2} - 14 x - 30 = 0$

Solve by factoring. Two numbers that multiply to $\left(- 30 \times 4\right) = - 120$ and that add to -14 are -20 and 6.

$4 {x}^{2} - 20 x + 6 x - 30 = 0$

$4 x \left(x - 5\right) + 6 \left(x - 5\right) = 0$

$\left(4 x + 6\right) \left(x - 5\right) = 0$

$x = - \frac{6}{4} \mathmr{and} 5$