# How do you solve (3x)/(x-6)=5+18/(x-6)?

Apr 14, 2018

$x = 6$

#### Explanation:

First make the five into a fraction and then add the two fractions together.

$\frac{3 x}{x - 6} = \frac{5 \left(x - 6\right)}{x - 6} + \frac{18}{x - 6}$

$\frac{3 x}{x - 6} = \frac{5 \left(x - 6\right) + 18}{x - 6}$

$\frac{3 x}{x - 6} = \frac{5 x - 30 + 18}{x - 6}$

$\frac{3 x}{x - 6} = \frac{5 x - 12}{x - 6}$

Cross multiply to make a linear equation.

$3 x \left(x - 6\right) = \left(5 x - 12\right) \left(x - 6\right)$

Cancel out the $\left(x - 6\right)$ on both sides and then simplify to solve for $x$.

$3 x = 5 x - 12 \to 5 x - 3 x = 12$

$2 x = 12$

$x = 6$

Apr 14, 2018

$x = 6$

#### Explanation:

Solve:

$\frac{3 x}{x - 6} = 5 + \frac{18}{x - 6}$

Multiply both sides by the least common denominator $\left(x - 6\right)$.

$\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - 6\right)}}} \times \frac{3 x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - 6\right)}}}} = 5 \left(x - 6\right) + \frac{18}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - 6\right)}}}} \times \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - 6\right)}}}$

Simplify.

$3 x = 5 \left(x - 6\right) + 18$

Expand.

$3 x = 5 x - 30 + 18$

Simplify.

$3 x = 5 x - 12$

Subtract $5 x$ from both sides.

$3 x - 5 x = - 12$

Simplify.

$- 2 x = - 12$

Divide both sides by $- 2$.

$\frac{{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}}}^{1} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}}} ^ 1 = {\left(\textcolor{red}{\cancel{\textcolor{b l a c k}{- 12}}}\right)}^{6} / {\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(- 2\right)}}}}^{1}$ $\leftarrow$ Two negatives make a positive.

Simplify.

$x = 6$