Simplify 4/(x-2)+11/(2(x-2))

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

Step 1

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

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

Step 2

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

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

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

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

Multiply $4$ by $2$ .

$\frac{8 + 11}{2 (x - 2)}$

Add $8$ and $11$ .

$\frac{19}{2 (x - 2)}$