# How do you solve 1/(x+4)-2=(3x-2)/(x+4)?

Nov 13, 2016

$x = - 1$

#### Explanation:

$\frac{1}{x + 4} - 2 = \frac{3 x - 2}{x + 4}$

Get a common denominator by multiplying the 2nd term by $\frac{x + 4}{x + 4}$

$\frac{1}{x + 4} - \frac{2 \cdot \left(x + 4\right)}{\left(x + 4\right)} = \frac{3 x - 2}{x + 4}$

$\frac{1}{x + 4} - \frac{\left(2 x + 8\right)}{x + 4} = \frac{3 x - 2}{x + 4}$

Compare to a simple equation like $\frac{1}{5} + \frac{2}{5} = \frac{x}{5}$
Because there is a common denominator, this can be solve with the numerators only $1 + 2 = x$

Similarly, solve the equation using only the numerators.

$1 - \left(2 x + 8\right) = 3 x - 2$

Distribute the negative.

$1 - 2 x - 8 = 3 x - 2$

$- 2 x - 7 = \textcolor{w h i t e}{a a} 3 x - 2$
$+ 2 x + 2 = + 2 x + 2$

$- 5 = 5 x$

$- \frac{5}{5} = \frac{5 x}{5}$

$- 1 = x$

When solving rational equations, it is important to check for extraneous solutions (solutions that "don't work" or result in division by zero).

$\frac{1}{- 1 + 4} - 2 = \frac{3 \left(- 1\right) - 2}{- 1 + 4} \textcolor{w h i t e}{a a a}$True