Solve x/2(x/3+2)

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

Evaluate

$$\frac{x^{2}}{6}+x$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{3}{3}.

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

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

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

Do the multiplications in x+2\times 3.

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

Multiply \frac{x}{2} times \frac{x+6}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x\left(x+6\right)}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{x\left(x+6\right)}{6}$$

Use the distributive property to multiply x by x+6.

$$\frac{x^{2}+6x}{6}$$

Expand

$$\frac{x^{2}}{6}+x$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{3}{3}.

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

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

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

Do the multiplications in x+2\times 3.

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

Multiply \frac{x}{2} times \frac{x+6}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x\left(x+6\right)}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{x\left(x+6\right)}{6}$$

Use the distributive property to multiply x by x+6.

$$\frac{x^{2}+6x}{6}$$