Simplify 3/(a-5)+(a+2)/a

$\frac{3}{a - 5} + \frac{a + 2}{a}$

To write $\frac{3}{a - 5}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$\frac{3}{a - 5} \cdot \frac{a}{a} + \frac{a + 2}{a}$

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

$\frac{3}{a - 5} \cdot \frac{a}{a} + \frac{a + 2}{a} \cdot \frac{a - 5}{a - 5}$

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

Multiply $\frac{3}{a - 5}$ by $\frac{a}{a}$ .

$\frac{3 a}{(a - 5) a} + \frac{a + 2}{a} \cdot \frac{a - 5}{a - 5}$

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

$\frac{3 a}{(a - 5) a} + \frac{(a + 2) (a - 5)}{a (a - 5)}$

Reorder the factors of $(a - 5) a$ .

$\frac{3 a}{a (a - 5)} + \frac{(a + 2) (a - 5)}{a (a - 5)}$

Combine the numerators over the common denominator.

$\frac{3 a + (a + 2) (a - 5)}{a (a - 5)}$

Simplify the numerator.

Expand $(a + 2) (a - 5)$ using the FOIL Method.

Apply the distributive property.

$\frac{3 a + a (a - 5) + 2 (a - 5)}{a (a - 5)}$

Apply the distributive property.

$\frac{3 a + a \cdot a + a \cdot - 5 + 2 (a - 5)}{a (a - 5)}$

Apply the distributive property.

$\frac{3 a + a \cdot a + a \cdot - 5 + 2 a + 2 \cdot - 5}{a (a - 5)}$

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ .

$\frac{3 a + a^{2} + a \cdot - 5 + 2 a + 2 \cdot - 5}{a (a - 5)}$

Move $- 5$ to the left of $a$ .

$\frac{3 a + a^{2} - 5 \cdot a + 2 a + 2 \cdot - 5}{a (a - 5)}$

Multiply $2$ by $- 5$ .

$\frac{3 a + a^{2} - 5 a + 2 a - 10}{a (a - 5)}$

Add $- 5 a$ and $2 a$ .

$\frac{3 a + a^{2} - 3 a - 10}{a (a - 5)}$

Subtract $3 a$ from $3 a$ .

$\frac{a^{2} + 0 - 10}{a (a - 5)}$

Add $a^{2}$ and $0$ .

$\frac{a^{2} - 10}{a (a - 5)}$