How do you solve $\frac{5}{x + 4} = \frac{5}{3 (x + 1)}$ $5/(x+4) = 5/(3(x+1))$ ?

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Answer 1 · 2015-10-20T18:05:57

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

In order to solve

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

Begin by dividing both sides by 5.

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

Then take the reciprocal of both sides:

$x + 4 = 3 (x + 1)$ $x+4 = 3(x+1)$

Expand the term on the right to be:

$x + 4 = 3 x + 3$ $x+4 = 3x+3$

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

$1 = 2 x$ $1 = 2x$

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

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

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

$\frac{5}{4.5} = \frac{5}{\frac{3}{2} + 3}$ $5/(4.5) = 5/(3/2+3)$

$\frac{5}{4.5} = \frac{5}{4.5}$ $5/(4.5) = 5/(4.5)$

How do you solve 5x+4=53(x+1)5/(x+4) = 5/(3(x+1))?