# Question 82ba7

Apr 14, 2017

$x = - 4$

#### Explanation:

Use the method of $\textcolor{b l u e}{\text{cross- multiplying}}$

$\text{Given " a/b=c/d" then}$

•color(white)(xx) ad=bc#

$\Rightarrow \frac{3}{x + 1} = \frac{5}{x - 1}$

$\Rightarrow 5 \left(x + 1\right) = 3 \left(x - 1\right)$

distributing gives.

$5 x + 5 = 3 x - 3$

$\text{subtract 3x from both sides}$

$5 x - 3 x + 5 = \cancel{3 x} \cancel{- 3 x} - 3$

$\Rightarrow 2 x + 5 = - 3$

$\text{subtract 5 from both sides.}$

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

$\Rightarrow 2 x = - 8$

$\text{divide both sides by 2}$

$\frac{\cancel{2} x}{\cancel{2}} = \frac{- 8}{2}$

$\Rightarrow x = - 4$

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

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

$\text{left side } = \frac{3}{- 4 + 1} = \frac{3}{- 3} = - 1$

$\text{right side } = \frac{5}{- 4 - 1} = \frac{5}{- 5} = - 1$

$\Rightarrow x = - 4 \text{ is the solution}$