Simplify (x/2+x/3)*6/x

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

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

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

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

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

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $2$ by $3$ .

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

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

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

Multiply $3$ by $2$ .

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

Combine the numerators over the common denominator.

$\frac{x \cdot 3 + x \cdot 2}{6} \cdot \frac{6}{x}$

Simplify the numerator.

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

$\frac{3 \cdot x + x \cdot 2}{6} \cdot \frac{6}{x}$

Move $2$ to the left of $x$ .

$\frac{3 x + 2 \cdot x}{6} \cdot \frac{6}{x}$

Add $3 x$ and $2 x$ .

$\frac{5 x}{6} \cdot \frac{6}{x}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x$ .

Factor $x$ out of $5 x$ .

$\frac{x \cdot 5}{6} \cdot \frac{6}{x}$

Cancel the common factor.

$\frac{x \cdot 5}{6} \cdot \frac{6}{x}$

Rewrite the expression.

$\frac{5}{6} \cdot 6$

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{5}{6} \cdot 6$

Rewrite the expression.

$5$