Simplify 2x+5+1/(x+7)

$2 x + 5 + \frac{1}{x + 7}$

Find the common denominator.

Write $2 x$ as a fraction with denominator $1$ .

$\frac{2 x}{1} + 5 + \frac{1}{x + 7}$

Multiply $\frac{2 x}{1}$ by $\frac{x + 7}{x + 7}$ .

$\frac{2 x}{1} \cdot \frac{x + 7}{x + 7} + 5 + \frac{1}{x + 7}$

Multiply $\frac{2 x}{1}$ by $\frac{x + 7}{x + 7}$ .

$\frac{2 x (x + 7)}{x + 7} + 5 + \frac{1}{x + 7}$

Write $5$ as a fraction with denominator $1$ .

$\frac{2 x (x + 7)}{x + 7} + \frac{5}{1} + \frac{1}{x + 7}$

Multiply $\frac{5}{1}$ by $\frac{x + 7}{x + 7}$ .

$\frac{2 x (x + 7)}{x + 7} + \frac{5}{1} \cdot \frac{x + 7}{x + 7} + \frac{1}{x + 7}$

Multiply $\frac{5}{1}$ by $\frac{x + 7}{x + 7}$ .

$\frac{2 x (x + 7)}{x + 7} + \frac{5 (x + 7)}{x + 7} + \frac{1}{x + 7}$

Combine the numerators over the common denominator.

$\frac{2 x (x + 7) + 5 (x + 7) + 1}{x + 7}$

Simplify each term.

Apply the distributive property.

$\frac{2 x \cdot x + 2 x \cdot 7 + 5 (x + 7) + 1}{x + 7}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{2 (x \cdot x) + 2 x \cdot 7 + 5 (x + 7) + 1}{x + 7}$

Multiply $x$ by $x$ .

$\frac{2 x^{2} + 2 x \cdot 7 + 5 (x + 7) + 1}{x + 7}$

Multiply $7$ by $2$ .

$\frac{2 x^{2} + 14 x + 5 (x + 7) + 1}{x + 7}$

Apply the distributive property.

$\frac{2 x^{2} + 14 x + 5 x + 5 \cdot 7 + 1}{x + 7}$

Multiply $5$ by $7$ .

$\frac{2 x^{2} + 14 x + 5 x + 35 + 1}{x + 7}$

Simplify by adding terms.

Add $14 x$ and $5 x$ .

$\frac{2 x^{2} + 19 x + 35 + 1}{x + 7}$

Add $35$ and $1$ .

$\frac{2 x^{2} + 19 x + 36}{x + 7}$