Simplify (6x)/(x+4)+2/(x-4)

$\frac{6 x}{x + 4} + \frac{2}{x - 4}$

Step 1

To write $\frac{6 x}{x + 4}$ as a fraction with a common denominator, multiply by $\frac{x - 4}{x - 4}$ .

$\frac{6 x}{x + 4} \cdot \frac{x - 4}{x - 4} + \frac{2}{x - 4}$

Step 2

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

$\frac{6 x}{x + 4} \cdot \frac{x - 4}{x - 4} + \frac{2}{x - 4} \cdot \frac{x + 4}{x + 4}$

Step 3

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

Multiply $\frac{6 x}{x + 4}$ by $\frac{x - 4}{x - 4}$ .

$\frac{6 x (x - 4)}{(x + 4) (x - 4)} + \frac{2}{x - 4} \cdot \frac{x + 4}{x + 4}$

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

$\frac{6 x (x - 4)}{(x + 4) (x - 4)} + \frac{2 (x + 4)}{(x - 4) (x + 4)}$

Reorder the factors of $(x - 4) (x + 4)$ .

$\frac{6 x (x - 4)}{(x + 4) (x - 4)} + \frac{2 (x + 4)}{(x + 4) (x - 4)}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 x (x - 4) + 2 (x + 4)}{(x + 4) (x - 4)}$

Step 5

Simplify the numerator.

Factor $2$ out of $6 x (x - 4) + 2 (x + 4)$ .

Factor $2$ out of $6 x (x - 4)$ .

$\frac{2 (3 x (x - 4)) + 2 (x + 4)}{(x + 4) (x - 4)}$

Factor $2$ out of $2 (3 x (x - 4)) + 2 (x + 4)$ .

$\frac{2 (3 x (x - 4) + x + 4)}{(x + 4) (x - 4)}$

Apply the distributive property.

$\frac{2 (3 x \cdot x + 3 x \cdot - 4 + x + 4)}{(x + 4) (x - 4)}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{2 (3 (x \cdot x) + 3 x \cdot - 4 + x + 4)}{(x + 4) (x - 4)}$

Multiply $x$ by $x$ .

$\frac{2 (3 x^{2} + 3 x \cdot - 4 + x + 4)}{(x + 4) (x - 4)}$

Multiply $- 4$ by $3$ .

$\frac{2 (3 x^{2} - 12 x + x + 4)}{(x + 4) (x - 4)}$

Add $- 12 x$ and $x$ .

$\frac{2 (3 x^{2} - 11 x + 4)}{(x + 4) (x - 4)}$