Simplify (x+7)/(x+3)+(x-4)/3

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

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

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

To write $\frac{x - 4}{3}$ as a fraction with a common denominator, multiply by $\frac{x + 3}{x + 3}$ .

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

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

Multiply $\frac{x + 7}{x + 3}$ by $\frac{3}{3}$ .

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

Multiply $\frac{x - 4}{3}$ by $\frac{x + 3}{x + 3}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Move $3$ to the left of $x$ .

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

Multiply $7$ by $3$ .

$\frac{3 \cdot x + 21 + (x - 4) (x + 3)}{3 (x + 3)}$

Expand $(x - 4) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$\frac{3 x + 21 + x (x + 3) - 4 (x + 3)}{3 (x + 3)}$

Apply the distributive property.

$\frac{3 x + 21 + x \cdot x + x \cdot 3 - 4 (x + 3)}{3 (x + 3)}$

Apply the distributive property.

$\frac{3 x + 21 + x \cdot x + x \cdot 3 - 4 x - 4 \cdot 3}{3 (x + 3)}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$\frac{3 x + 21 + x^{2} + x \cdot 3 - 4 x - 4 \cdot 3}{3 (x + 3)}$

Move $3$ to the left of $x$ .

$\frac{3 x + 21 + x^{2} + 3 \cdot x - 4 x - 4 \cdot 3}{3 (x + 3)}$

Multiply $- 4$ by $3$ .

$\frac{3 x + 21 + x^{2} + 3 x - 4 x - 12}{3 (x + 3)}$

Subtract $4 x$ from $3 x$ .

$\frac{3 x + 21 + x^{2} - x - 12}{3 (x + 3)}$

Subtract $x$ from $3 x$ .

$\frac{2 x + 21 + x^{2} - 12}{3 (x + 3)}$

Subtract $12$ from $21$ .

$\frac{2 x + x^{2} + 9}{3 (x + 3)}$

Reorder terms.

$\frac{x^{2} + 2 x + 9}{3 (x + 3)}$