Simplify (3x)/(x+3)+(x-2)/x

$\frac{3 x}{x + 3} + \frac{x - 2}{x}$

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

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

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

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Expand $(x - 2) (x + 3)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $- 2$ by $3$ .

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

Subtract $2 x$ from $3 x$ .

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

Add $3 x^{2}$ and $x^{2}$ .

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