Evaluate 7/(x+2)+4/(x-5)

$\frac{7}{x + 2} + \frac{4}{x - 5}$

To write $\frac{7}{x + 2}$ as a fraction with a common denominator, multiply by $\frac{x - 5}{x - 5}$ .

$\frac{7}{x + 2} \cdot \frac{x - 5}{x - 5} + \frac{4}{x - 5}$

To write $\frac{4}{x - 5}$ as a fraction with a common denominator, multiply by $\frac{x + 2}{x + 2}$ .

$\frac{7}{x + 2} \cdot \frac{x - 5}{x - 5} + \frac{4}{x - 5} \cdot \frac{x + 2}{x + 2}$

Write each expression with a common denominator of $(x + 2) (x - 5)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7}{x + 2}$ by $\frac{x - 5}{x - 5}$ .

$\frac{7 (x - 5)}{(x + 2) (x - 5)} + \frac{4}{x - 5} \cdot \frac{x + 2}{x + 2}$

Multiply $\frac{4}{x - 5}$ by $\frac{x + 2}{x + 2}$ .

$\frac{7 (x - 5)}{(x + 2) (x - 5)} + \frac{4 (x + 2)}{(x - 5) (x + 2)}$

Reorder the factors of $(x - 5) (x + 2)$ .

$\frac{7 (x - 5)}{(x + 2) (x - 5)} + \frac{4 (x + 2)}{(x + 2) (x - 5)}$

Combine the numerators over the common denominator.

$\frac{7 (x - 5) + 4 (x + 2)}{(x + 2) (x - 5)}$

Simplify the numerator.

Apply the distributive property.

$\frac{7 x + 7 \cdot - 5 + 4 (x + 2)}{(x + 2) (x - 5)}$

Multiply $7$ by $- 5$ .

$\frac{7 x - 35 + 4 (x + 2)}{(x + 2) (x - 5)}$

Apply the distributive property.

$\frac{7 x - 35 + 4 x + 4 \cdot 2}{(x + 2) (x - 5)}$

Multiply $4$ by $2$ .

$\frac{7 x - 35 + 4 x + 8}{(x + 2) (x - 5)}$

Add $7 x$ and $4 x$ .

$\frac{11 x - 35 + 8}{(x + 2) (x - 5)}$

Add $- 35$ and $8$ .

$\frac{11 x - 27}{(x + 2) (x - 5)}$