Simplify (2x-7)/(x-2)+(8x)/(3x-6)

$\frac{2 x - 7}{x - 2} + \frac{8 x}{3 x - 6}$

Factor $3$ out of $3 x - 6$ .

Factor $3$ out of $3 x$ .

$\frac{2 x - 7}{x - 2} + \frac{8 x}{3 (x) - 6}$

Factor $3$ out of $- 6$ .

$\frac{2 x - 7}{x - 2} + \frac{8 x}{3 x + 3 \cdot - 2}$

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

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

To write $\frac{2 x - 7}{x - 2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Write each expression with a common denominator of $(x - 2) \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 x - 7}{x - 2}$ by $\frac{3}{3}$ .

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

Reorder the factors of $(x - 2) \cdot 3$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $3$ by $2$ .

$\frac{6 x - 7 \cdot 3 + 8 x}{3 (x - 2)}$

Multiply $- 7$ by $3$ .

$\frac{6 x - 21 + 8 x}{3 (x - 2)}$

Add $6 x$ and $8 x$ .

$\frac{14 x - 21}{3 (x - 2)}$

Factor $7$ out of $14 x - 21$ .

Factor $7$ out of $14 x$ .

$\frac{7 (2 x) - 21}{3 (x - 2)}$

Factor $7$ out of $- 21$ .

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

Factor $7$ out of $7 (2 x) + 7 (- 3)$ .

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