# How do you solve 5/(x+4) = 5/(3(x+1))?

Oct 20, 2015

The solution is $x = \frac{1}{2}$

#### Explanation:

In order to solve

$\frac{5}{x + 4} = \frac{5}{3 \left(x + 1\right)}$

Begin by dividing both sides by 5.

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

Then take the reciprocal of both sides:

$x + 4 = 3 \left(x + 1\right)$

Expand the term on the right to be:

$x + 4 = 3 x + 3$

Through some simple algebra you should be able to show that:

$1 = 2 x$

$\frac{1}{2} = x$

Checking the answer by substituting $\frac{1}{2}$ for x, we can see that both sides will be equal:

$\frac{5}{\frac{1}{2} + 4} = \frac{5}{3 \left(\frac{1}{2} + 1\right)}$

$\frac{5}{4.5} = \frac{5}{\frac{3}{2} + 3}$

$\frac{5}{4.5} = \frac{5}{4.5}$