# How do you solve 4/x+7=6/x?

Apr 6, 2018

The solution is $x = \frac{2}{7}$.

#### Explanation:

Multiply everything by $x$ to get rid of the $x$ in the denominator:

$\frac{4}{x} + 7 = \frac{6}{x}$

$\frac{4}{x} \textcolor{b l u e}{\cdot x} + 7 \textcolor{b l u e}{\cdot x} = \frac{6}{x} \textcolor{b l u e}{\cdot x}$

$\frac{4}{\textcolor{red}{\cancel{\textcolor{b l a c k}{x}}}} \textcolor{b l u e}{\cdot \textcolor{red}{\cancel{\textcolor{b l u e}{x}}}} + 7 \textcolor{b l u e}{\cdot x} = \frac{6}{\textcolor{red}{\cancel{\textcolor{b l a c k}{x}}}} \textcolor{b l u e}{\cdot \textcolor{red}{\cancel{\textcolor{b l u e}{x}}}}$

$4 + 7 \textcolor{b l u e}{\cdot x} = 6$

$4 + 7 x = 6$

$4 + 7 x \textcolor{b l u e}{-} \textcolor{b l u e}{4} = 6 \textcolor{b l u e}{-} \textcolor{b l u e}{4}$

$\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} + 7 x \textcolor{red}{\cancel{\textcolor{b l a c k}{\textcolor{b l u e}{-} \textcolor{b l u e}{4}}}} = 6 \textcolor{b l u e}{-} \textcolor{b l u e}{4}$

$7 x = 6 \textcolor{b l u e}{-} \textcolor{b l u e}{4}$

$7 x = 2$

$\textcolor{b l u e}{\frac{\textcolor{b l a c k}{7 x}}{7}} = \textcolor{b l u e}{\frac{\textcolor{b l a c k}{2}}{7}}$

$\textcolor{b l u e}{\frac{\textcolor{b l a c k}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} x}}{\textcolor{red}{\cancel{\textcolor{b l u e}{7}}}}} = \textcolor{b l u e}{\frac{\textcolor{b l a c k}{2}}{7}}$

$x = \textcolor{b l u e}{\frac{\textcolor{b l a c k}{2}}{7}}$

That's the solution. Hope this helped!

Apr 6, 2018

$\frac{2}{7}$

#### Explanation:

$\frac{4}{x} + 7 = \frac{6}{x}$

$\Rightarrow \frac{4}{x} - \frac{6}{x} = - 7$

$\Rightarrow \frac{4 - 6}{x} = - 7$

$\Rightarrow - \frac{2}{x} = - 7$

$\Rightarrow x = \frac{2}{7}$

Hope this helps :)