# How do you solve (x+5)/(x-1)=7/6?

Apr 23, 2018

$x = 37$

#### Explanation:

$\text{we can use "color(blue)"cross-multiplication ""to solve}$

$\text{given one fraction equal to another fraction then}$

•color(white)(x)a/b=c/drArrad=bclarrcolor(blue)"cross-multiplication"

$\frac{x + 5}{x - 1} = \frac{7}{6}$

$\Rightarrow 7 \left(x - 1\right) = 6 \left(x + 5\right) \leftarrow \textcolor{b l u e}{\text{distribute}}$

$\Rightarrow 7 x - 7 = 6 x + 30$

$\text{subtract 6x from both sides}$

$7 x - 6 x - 7 = \cancel{6 x} \cancel{- 6 x} + 30$

$\Rightarrow x - 7 = 30$

$\text{add 7 to both sides}$

$x \cancel{- 7} \cancel{+ 7} = 30 + 7$

$\textcolor{b l u e}{\text{As a check}}$

Substitute this value into the left side of the equation and if equal to the right side then it is the solution.

$\frac{37 + 5}{37 - 1} = \frac{42}{36} = \frac{7}{6} = \text{ right side}$

$\Rightarrow x = 37 \text{ is the solution}$