Solve p/2*(3/p+p/2)

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

Evaluate

$$\frac{p^{2}+6}{4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of p and 2 is 2p. Multiply \frac{3}{p} times \frac{2}{2}. Multiply \frac{p}{2} times \frac{p}{p}.

$$\frac{p}{2}\left(\frac{3\times 2}{2p}+\frac{pp}{2p}\right)$$

Since \frac{3\times 2}{2p} and \frac{pp}{2p} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3\times 2+pp.

$$\frac{p}{2}\times \frac{6+p^{2}}{2p}$$

Multiply \frac{p}{2} times \frac{6+p^{2}}{2p} by multiplying numerator times numerator and denominator times denominator.

$$\frac{p\left(6+p^{2}\right)}{2\times 2p}$$

Cancel out p in both numerator and denominator.

$$\frac{p^{2}+6}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{p^{2}+6}{4}$$

Expand

$$\frac{p^{2}}{4}+\frac{3}{2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of p and 2 is 2p. Multiply \frac{3}{p} times \frac{2}{2}. Multiply \frac{p}{2} times \frac{p}{p}.

$$\frac{p}{2}\left(\frac{3\times 2}{2p}+\frac{pp}{2p}\right)$$

Since \frac{3\times 2}{2p} and \frac{pp}{2p} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3\times 2+pp.

$$\frac{p}{2}\times \frac{6+p^{2}}{2p}$$

Multiply \frac{p}{2} times \frac{6+p^{2}}{2p} by multiplying numerator times numerator and denominator times denominator.

$$\frac{p\left(6+p^{2}\right)}{2\times 2p}$$

Cancel out p in both numerator and denominator.

$$\frac{p^{2}+6}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{p^{2}+6}{4}$$