Simplify x+3+(3x)/(x+5)

$x + 3 + \frac{3 x}{x + 5}$

Step 1

Find the common denominator.

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

$\frac{x}{1} + 3 + \frac{3 x}{x + 5}$

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

$\frac{x}{1} \cdot \frac{x + 5}{x + 5} + 3 + \frac{3 x}{x + 5}$

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

$\frac{x (x + 5)}{x + 5} + 3 + \frac{3 x}{x + 5}$

Write $3$ as a fraction with denominator $1$ .

$\frac{x (x + 5)}{x + 5} + \frac{3}{1} + \frac{3 x}{x + 5}$

Multiply $\frac{3}{1}$ by $\frac{x + 5}{x + 5}$ .

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

Multiply $\frac{3}{1}$ by $\frac{x + 5}{x + 5}$ .

$\frac{x (x + 5)}{x + 5} + \frac{3 (x + 5)}{x + 5} + \frac{3 x}{x + 5}$

Step 2

Combine the numerators over the common denominator.

$\frac{x (x + 5) + 3 (x + 5) + 3 x}{x + 5}$

Step 3

Simplify each term.

Apply the distributive property.

$\frac{x \cdot x + x \cdot 5 + 3 (x + 5) + 3 x}{x + 5}$

Multiply $x$ by $x$ .

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

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

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

Apply the distributive property.

$\frac{x^{2} + 5 x + 3 x + 3 \cdot 5 + 3 x}{x + 5}$

Multiply $3$ by $5$ .

$\frac{x^{2} + 5 x + 3 x + 15 + 3 x}{x + 5}$

Step 4

Simplify by adding terms.

Add $5 x$ and $3 x$ .

$\frac{x^{2} + 8 x + 15 + 3 x}{x + 5}$

Add $8 x$ and $3 x$ .

$\frac{x^{2} + 11 x + 15}{x + 5}$