# How do you solve 6/(t+2)=4/t?

Jan 16, 2017

See the entire solution process below:

#### Explanation:

First, we multiple each side of the equation by t(t + 2)# to eliminate the fractions and keep the equation balanced:

$t \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(t + 2\right)}}} \times \frac{6}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(t + 2\right)}}}} = \textcolor{red}{\cancel{\textcolor{b l a c k}{t}}} \left(t + 2\right) \times \frac{4}{\textcolor{red}{\cancel{\textcolor{b l a c k}{t}}}}$

$t \times 6 = \left(t + 2\right) \times 4$

$6 t = 4 t + 8$

Next, substract $\textcolor{red}{4 t}$ from each side of the equation to isolate the $t$ term while keeping the equation balanced:

$6 t - \textcolor{red}{4 t} = 4 t + 8 - \textcolor{red}{4 t}$

$\left(6 - 4\right) t = 4 t - \textcolor{red}{4 t} + 8$

$2 t = 0 + 8$

$2 t = 8$

Now, divide each side of the equation by $\textcolor{red}{2}$ to solve for $t$:

$\frac{2 t}{\textcolor{red}{2}} = \frac{8}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} t}{\cancel{\textcolor{red}{2}}} = 4$

$t = 4$