# How do you solve 8/(x+2)+8/2=5?

May 26, 2017

$x = 6$

#### Explanation:

Given: $\frac{8}{x + 2} + \frac{8}{2} = 5$

One way to solve is by realizing that $\frac{8}{2} = 4$, so substitute this value into the equation: $\text{ } \frac{8}{x + 2} + 4 = 5$

Simplify by subtracting $4$ from both sides of the equation:
$\frac{8}{x + 2} + 4 - 4 = 5 - 4$;

$\frac{8}{x + 2} = 1$

Multiply both sides of the equation by $x + 2$:

$\cancel{x + 2} \cdot \frac{8}{\cancel{x + 2}} = 1 \cdot \left(x + 2\right)$

Simplify: $\text{ } 8 = x + 2$

Subtract both sides of the equation by $2$:

$8 - 2 = x + 2 - 2$

$6 = x$

A second way to solve is by finding a common denominator for both sides of the equation $2 \left(x + 2\right)$:

$\frac{8}{x + 2} \cdot \frac{2}{2} + \frac{8}{2} \cdot \frac{x + 2}{x + 2} = 5 \cdot \frac{2 \left(x + 2\right)}{2 \left(x + 2\right)}$

Simplify:

$\frac{16 + 8 \left(x + 2\right)}{2 \left(x + 2\right)} = \frac{10 \left(x + 2\right)}{2 \left(x + 2\right)}$

Since both denominators are equal, we can set the numerators equal to solve:

$16 + 8 \left(x + 2\right) = 10 \left(x + 2\right)$

Distribute:

$16 + 8 x + 16 = 10 x + 20$

Add like terms on the same side:

$32 + 8 x = 10 x + 20$

Subtract $20$ from both sides:

$32 - 20 + 8 x = 10 x + 20 - 20$

$12 + 8 x = 10 x$

Subtract $8 x$ from both sides: $\text{ } 12 + 8 x - 8 x = 10 x - 8 x$

Simplify: $\text{ } 12 = 2 x$

Divide both sides by $2 : \text{ } \frac{12}{2} = \frac{2 x}{2}$

Simplify: $\text{ } 6 = x$