Simplify (4x)/(x-7)-(3x)/(2x-14)

$\frac{4 x}{x - 7} - \frac{3 x}{2 x - 14}$

Step 1

Factor $2$ out of $2 x - 14$ .

Factor $2$ out of $2 x$ .

$\frac{4 x}{x - 7} - \frac{3 x}{2 (x) - 14}$

Factor $2$ out of $- 14$ .

$\frac{4 x}{x - 7} - \frac{3 x}{2 x + 2 \cdot - 7}$

Factor $2$ out of $2 x + 2 \cdot - 7$ .

$\frac{4 x}{x - 7} - \frac{3 x}{2 (x - 7)}$

Step 2

To write $\frac{4 x}{x - 7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 x}{x - 7} \cdot \frac{2}{2} - \frac{3 x}{2 (x - 7)}$

Step 3

Write each expression with a common denominator of $(x - 7) \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4 x}{x - 7}$ by $\frac{2}{2}$ .

$\frac{4 x \cdot 2}{(x - 7) \cdot 2} - \frac{3 x}{2 (x - 7)}$

Reorder the factors of $(x - 7) \cdot 2$ .

$\frac{4 x \cdot 2}{2 (x - 7)} - \frac{3 x}{2 (x - 7)}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 x \cdot 2 - 3 x}{2 (x - 7)}$

Step 5

Simplify the numerator.

Factor $x$ out of $4 x \cdot 2 - 3 x$ .

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

$\frac{x (4 \cdot 2) - 3 x}{2 (x - 7)}$

Factor $x$ out of $- 3 x$ .

$\frac{x (4 \cdot 2) + x \cdot - 3}{2 (x - 7)}$

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

$\frac{x (4 \cdot 2 - 3)}{2 (x - 7)}$

Multiply $4$ by $2$ .

$\frac{x (8 - 3)}{2 (x - 7)}$

Subtract $3$ from $8$ .

$\frac{x \cdot 5}{2 (x - 7)}$

Step 6

Move $5$ to the left of $x$ .

$\frac{5 x}{2 (x - 7)}$