Simplify (x+2)/(2x-2)+(4x-3)/(10x-10)

$\frac{x + 2}{2 x - 2} + \frac{4 x - 3}{10 x - 10}$

Simplify each term.

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

Factor $2$ out of $2 x$ .

$\frac{x + 2}{2 (x) - 2} + \frac{4 x - 3}{10 x - 10}$

Factor $2$ out of $- 2$ .

$\frac{x + 2}{2 (x) + 2 (- 1)} + \frac{4 x - 3}{10 x - 10}$

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

$\frac{x + 2}{2 (x - 1)} + \frac{4 x - 3}{10 x - 10}$

Factor $10$ out of $10 x - 10$ .

Factor $10$ out of $10 x$ .

$\frac{x + 2}{2 (x - 1)} + \frac{4 x - 3}{10 (x) - 10}$

Factor $10$ out of $- 10$ .

$\frac{x + 2}{2 (x - 1)} + \frac{4 x - 3}{10 (x) + 10 (- 1)}$

Factor $10$ out of $10 (x) + 10 (- 1)$ .

$\frac{x + 2}{2 (x - 1)} + \frac{4 x - 3}{10 (x - 1)}$

To write $\frac{x + 2}{2 (x - 1)}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x + 2}{2 (x - 1)} \cdot \frac{5}{5} + \frac{4 x - 3}{10 (x - 1)}$

Write each expression with a common denominator of $10 (x - 1)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x + 2}{2 (x - 1)}$ by $\frac{5}{5}$ .

$\frac{(x + 2) \cdot 5}{2 (x - 1) \cdot 5} + \frac{4 x - 3}{10 (x - 1)}$

Multiply $5$ by $2$ .

$\frac{(x + 2) \cdot 5}{10 (x - 1)} + \frac{4 x - 3}{10 (x - 1)}$

Combine the numerators over the common denominator.

$\frac{(x + 2) \cdot 5 + 4 x - 3}{10 (x - 1)}$

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 5 + 2 \cdot 5 + 4 x - 3}{10 (x - 1)}$

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

$\frac{5 \cdot x + 2 \cdot 5 + 4 x - 3}{10 (x - 1)}$

Multiply $2$ by $5$ .

$\frac{5 \cdot x + 10 + 4 x - 3}{10 (x - 1)}$

Add $5 x$ and $4 x$ .

$\frac{9 x + 10 - 3}{10 (x - 1)}$

Subtract $3$ from $10$ .

$\frac{9 x + 7}{10 (x - 1)}$