Simplify (5x)/(x+2)-(4x+3)/(3x+6)

$\frac{5 x}{x + 2} - \frac{4 x + 3}{3 x + 6}$

Factor $3$ out of $3 x + 6$ .

Factor $3$ out of $3 x$ .

$\frac{5 x}{x + 2} - \frac{4 x + 3}{3 (x) + 6}$

Factor $3$ out of $6$ .

$\frac{5 x}{x + 2} - \frac{4 x + 3}{3 x + 3 \cdot 2}$

Factor $3$ out of $3 x + 3 \cdot 2$ .

$\frac{5 x}{x + 2} - \frac{4 x + 3}{3 (x + 2)}$

To write $\frac{5 x}{x + 2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 x}{x + 2} \cdot \frac{3}{3} - \frac{4 x + 3}{3 (x + 2)}$

Write each expression with a common denominator of $(x + 2) \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 x}{x + 2}$ by $\frac{3}{3}$ .

$\frac{5 x \cdot 3}{(x + 2) \cdot 3} - \frac{4 x + 3}{3 (x + 2)}$

Reorder the factors of $(x + 2) \cdot 3$ .

$\frac{5 x \cdot 3}{3 (x + 2)} - \frac{4 x + 3}{3 (x + 2)}$

Combine the numerators over the common denominator.

$\frac{5 x \cdot 3 - (4 x + 3)}{3 (x + 2)}$

Simplify the numerator.

Multiply $3$ by $5$ .

$\frac{15 x - (4 x + 3)}{3 (x + 2)}$

Apply the distributive property.

$\frac{15 x - (4 x) - 1 \cdot 3}{3 (x + 2)}$

Multiply $4$ by $- 1$ .

$\frac{15 x - 4 x - 1 \cdot 3}{3 (x + 2)}$

Multiply $- 1$ by $3$ .

$\frac{15 x - 4 x - 3}{3 (x + 2)}$

Subtract $4 x$ from $15 x$ .

$\frac{11 x - 3}{3 (x + 2)}$