# How do you solve 3/(4x)=5/(x+2)?

Oct 7, 2016

$x = \frac{6}{17}$

#### Explanation:

In order to get rid of the $x$'s in the denominators you have to multiply them over to the other side:

$\frac{3 \left(\textcolor{b l u e}{x + 2}\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4 x}}}} = \frac{5 \left(\textcolor{b l u e}{4 x}\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{x + 2}}}}$

Multiply it out:

$3 x + 6 = 20 x$

Subtract the $3 x$ to the other side and add the $20 x$ and $3 x$:

$\textcolor{red}{\cancel{\textcolor{b l a c k}{3 x}}} + 6 = 20 x - \textcolor{b l u e}{3 x}$

$6 = 17 x$

Then divide $6$ by $17$:

$x = \frac{6}{17}$