Simplify (1/p+2/3)/(1/p)

$\frac{\frac{1}{p} + \frac{2}{3}}{\frac{1}{p}}$

Multiply the numerator by the reciprocal of the denominator.

$(\frac{1}{p} + \frac{2}{3}) p$

To write $\frac{1}{p}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{1}{p} \cdot \frac{3}{3} + \frac{2}{3}) p$

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

$(\frac{1}{p} \cdot \frac{3}{3} + \frac{2}{3} \cdot \frac{p}{p}) p$

Write each expression with a common denominator of $p \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{p}$ by $\frac{3}{3}$ .

$(\frac{3}{p \cdot 3} + \frac{2}{3} \cdot \frac{p}{p}) p$

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

$(\frac{3}{p \cdot 3} + \frac{2 p}{3 p}) p$

Reorder the factors of $p \cdot 3$ .

$(\frac{3}{3 p} + \frac{2 p}{3 p}) p$

Combine the numerators over the common denominator.

$\frac{3 + 2 p}{3 p} p$

Cancel the common factor of $p$ .

Factor $p$ out of $3 p$ .

$\frac{3 + 2 p}{p \cdot 3} p$

Cancel the common factor.

$\frac{3 + 2 p}{p \cdot 3} p$

Rewrite the expression.

$\frac{3 + 2 p}{3}$