# Question #e9fb6

Nov 13, 2016

$x = \frac{5}{8}$

#### Explanation:

Given:$\text{ } \frac{\sqrt{2 x + 1}}{\sqrt{2 x - 1}} = 3$

Square both sides giving:

$\frac{2 x + 1}{2 x - 1} = 9$

Multiply both sides by $\left(2 x + 1\right)$

$2 x + 1 = 9 \left(2 x - 1\right)$

$2 x + 1 = 18 x - 9$

Subtract $2 x$ from both sides

$1 = 16 x - 9$

$10 = 16 x$

Divide both sides by 16

$\frac{10}{16} = x$

Write as: $x = \frac{10}{16} \equiv \frac{10 \div 2}{16 \div 2} = \frac{5}{8}$

Nov 13, 2016

$x = \frac{5}{8}$

#### Explanation:

Square both sides and solve

$\frac{\sqrt{2 x + 1}}{\sqrt{2 x - 1}} = 3 \text{ }$square both sides to get:

$\frac{2 x + 1}{2 x - 1} = 9 \text{ }$from which:

$2 x + 1 = 18 x - 9 \text{ }$collect like terms to get:

$10 = 16 x \text{ }$which yields

$x = \frac{10}{16} = \frac{5}{8}$