# How do you solve for x: 12/(x+1) - 10/(x-3)=-3?

Jun 25, 2016

$x = 5 \mathmr{and} x = - \frac{11}{3}$

#### Explanation:

In an equation, we can get rid of the denominators by multiplying every term by the LCM of the denominators.

The LCM is this case is $\textcolor{red}{\left(x + 1\right) \left(x - 3\right)}$

$\frac{12 \times \textcolor{red}{\cancel{\left(x + 1\right)} \left(x - 3\right)}}{\cancel{\left(x + 1\right)}} - \frac{10 \times \textcolor{red}{\left(x + 1\right) \cancel{\left(x - 3\right)}}}{\cancel{\left(x - 3\right)}} = - 3 \textcolor{red}{\left(x + 1\right) \left(x - 3\right)}$

12(x-3) - 10(x+1) = -3(x+1)(x-3))

$12 x - 36 - 10 x - 10 = - 3 \left({x}^{2} - 2 x - 3\right)$

$2 x - 46 = - 3 {x}^{2} + 6 x + 9$

$3 {x}^{2} - 4 x - 55 = 0 \text{ now factorise}$

$\left(3 x + 11\right) \left(x - 5\right) = 0$

If $3 x + 11 = 0 , \Rightarrow x = - \frac{11}{3}$

If $x - 5 = \Rightarrow x = 5$