Simplify (2x)/(x-9)-x/(2(x-9))

$\frac{2 x}{x - 9} - \frac{x}{2 (x - 9)}$

Step 1

To write $\frac{2 x}{x - 9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 x}{x - 9} \cdot \frac{2}{2} - \frac{x}{2 (x - 9)}$

Step 2

Write each expression with a common denominator of $(x - 9) \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 x}{x - 9}$ by $\frac{2}{2}$ .

$\frac{2 x \cdot 2}{(x - 9) \cdot 2} - \frac{x}{2 (x - 9)}$

Reorder the factors of $(x - 9) \cdot 2$ .

$\frac{2 x \cdot 2}{2 (x - 9)} - \frac{x}{2 (x - 9)}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 x \cdot 2 - x}{2 (x - 9)}$

Step 4

Simplify the numerator.

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

Factor $x$ out of $2 x \cdot 2$ .

$\frac{x (2 \cdot 2) - x}{2 (x - 9)}$

Factor $x$ out of $- x$ .

$\frac{x (2 \cdot 2) + x \cdot - 1}{2 (x - 9)}$

Factor $x$ out of $x (2 \cdot 2) + x \cdot - 1$ .

$\frac{x (2 \cdot 2 - 1)}{2 (x - 9)}$

Multiply $2$ by $2$ .

$\frac{x (4 - 1)}{2 (x - 9)}$

Subtract $1$ from $4$ .

$\frac{x \cdot 3}{2 (x - 9)}$

Step 5

Move $3$ to the left of $x$ .

$\frac{3 x}{2 (x - 9)}$