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

May 21, 2017

See a solution process below:

#### Explanation:

First, we can multiply each side of the equation by $\textcolor{red}{12} \textcolor{b l u e}{x}$ to eliminate the fractions while keeping the equation balanced. $\textcolor{red}{12} \textcolor{b l u e}{x}$ is the Least Common Denominator for the three fractions:

$\textcolor{red}{12} \textcolor{b l u e}{x} \left(\left(\frac{1}{4}\right) + \left(\frac{1}{x}\right)\right) = \textcolor{red}{12} \textcolor{b l u e}{x} \times \left(\frac{1}{3}\right)$

$\left(\textcolor{red}{12} \textcolor{b l u e}{x} \times \left(\frac{1}{4}\right)\right) + \left(\textcolor{red}{12} \textcolor{b l u e}{x} \times \left(\frac{1}{x}\right)\right) = \cancel{\textcolor{red}{12}} 4 \textcolor{b l u e}{x} \times \left(\frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}\right)$

$\left(\cancel{\textcolor{red}{12}} 3 \textcolor{b l u e}{x} \times \left(\frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}}\right)\right) + \left(\textcolor{red}{12} \cancel{\textcolor{b l u e}{x}} \times \left(\frac{1}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{x}}}}\right)\right) = 4 x$

$3 x + 12 = 4 x$

Now, subtract $\textcolor{red}{3 x}$ from each side of the equation to solve for $x$ while keeping the equation balanced:

$- \textcolor{red}{3 x} + 3 x + 12 = - \textcolor{red}{3 x} + 4 x$

$0 + 12 = \left(- \textcolor{red}{3} + 4\right) x$

$12 = 1 x$

$12 = x$

$x = 12$