Simplify (5x)/(4x-8)+(x+2)/(x-2)

$\frac{5 x}{4 x - 8} + \frac{x + 2}{x - 2}$

Factor $4$ out of $4 x - 8$ .

Factor $4$ out of $4 x$ .

$\frac{5 x}{4 (x) - 8} + \frac{x + 2}{x - 2}$

Factor $4$ out of $- 8$ .

$\frac{5 x}{4 x + 4 \cdot - 2} + \frac{x + 2}{x - 2}$

Factor $4$ out of $4 x + 4 \cdot - 2$ .

$\frac{5 x}{4 (x - 2)} + \frac{x + 2}{x - 2}$

To write $\frac{x + 2}{x - 2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 x}{4 (x - 2)} + \frac{x + 2}{x - 2} \cdot \frac{4}{4}$

Write each expression with a common denominator of $4 (x - 2)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x + 2}{x - 2}$ by $\frac{4}{4}$ .

$\frac{5 x}{4 (x - 2)} + \frac{(x + 2) \cdot 4}{(x - 2) \cdot 4}$

Reorder the factors of $(x - 2) \cdot 4$ .

$\frac{5 x}{4 (x - 2)} + \frac{(x + 2) \cdot 4}{4 (x - 2)}$

Combine the numerators over the common denominator.

$\frac{5 x + (x + 2) \cdot 4}{4 (x - 2)}$

Simplify the numerator.

Apply the distributive property.

$\frac{5 x + x \cdot 4 + 2 \cdot 4}{4 (x - 2)}$

Move $4$ to the left of $x$ .

$\frac{5 x + 4 \cdot x + 2 \cdot 4}{4 (x - 2)}$

Multiply $2$ by $4$ .

$\frac{5 x + 4 \cdot x + 8}{4 (x - 2)}$

Add $5 x$ and $4 x$ .

$\frac{9 x + 8}{4 (x - 2)}$