# 5/3-2/x=8/x?

## if x was not equal to 0

Feb 26, 2018

$x = 6$

#### Explanation:

$\frac{5}{3} - \frac{2}{x} = \frac{8}{x} | \textcolor{b l u e}{\cdot x}$
$\frac{5}{3} \textcolor{b l u e}{\cdot x} - \frac{2}{\cancel{x}} \cancel{\textcolor{b l u e}{\cdot x}} = \frac{8}{\cancel{x}} \cancel{\textcolor{b l u e}{\cdot x}}$
$\frac{5}{3} x - 2 = 8 | \textcolor{b l u e}{+ 2}$
$\frac{5}{3} x \cancel{- 2 \textcolor{b l u e}{+ 2}} = 8 \textcolor{b l u e}{+ 2}$
$\frac{5}{3} x = 10 | \textcolor{b l u e}{\cdot \frac{3}{5}}$
$\cancel{\frac{5}{3} \textcolor{b l u e}{\cdot \frac{3}{5}}} \cdot x = 2 \cancel{10} \textcolor{b l u e}{\cdot \frac{3}{\cancel{5}}}$
$x = 6$

Feb 26, 2018

$x = 6$

#### Explanation:

First, ensure that all terms with $x$ in the denominator are on the same side. This entails adding $\frac{2}{x}$ to each side:

$\frac{5}{3} \cancel{- \frac{2}{x} + \frac{2}{x}} = \frac{8}{x} + \frac{2}{x}$

Since the terms on the right have a common denominator, we can add:

$\frac{5}{3} = \frac{8 + 2}{x}$

$\frac{5}{3} = \frac{10}{x}$

Multiply each term by the term diagonal to it:

$5 x = 10 \left(3\right)$

$5 x = 30$

Divide each side by $5 :$

$\frac{\cancel{5} x}{\cancel{5}} = \frac{30}{5}$

$x = 6$

Feb 26, 2018

$\frac{5}{3} - \frac{2}{x} = \frac{8}{x}$

$\frac{5}{3} \cancel{- \frac{2}{x}} \cancel{+ \frac{2}{x}} = \frac{8}{x} + \frac{2}{x}$

$\frac{5}{3} = \frac{10}{x}$

$\frac{5}{3} \cdot x = \frac{10}{\cancel{x}} \cdot \cancel{x}$$\to$$\frac{5}{3} x = 10$

$\cancel{\frac{5}{3}} x \cdot \cancel{\frac{3}{5}} = 10 \cdot \frac{3}{5}$

$x = 6$

Hope that helped!
~Chandler Dowd