Solve 1/2(1/3-1/2n+3)

$$\frac { 1 } { 2 } ( \frac { 1 } { 3 } - \frac { 1 } { 2 n + 3 } )$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2n+3 is 3\left(2n+3\right). Multiply \frac{1}{3} times \frac{2n+3}{2n+3}. Multiply \frac{1}{2n+3} times \frac{3}{3}.

$$\frac{1}{2}\left(\frac{2n+3}{3\left(2n+3\right)}-\frac{3}{3\left(2n+3\right)}\right)$$

Since \frac{2n+3}{3\left(2n+3\right)} and \frac{3}{3\left(2n+3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\times \frac{2n+3-3}{3\left(2n+3\right)}$$

Combine like terms in 2n+3-3.

$$\frac{1}{2}\times \frac{2n}{3\left(2n+3\right)}$$

Multiply \frac{1}{2} times \frac{2n}{3\left(2n+3\right)} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

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

Use the distributive property to multiply 3 by 2n+3.

$$\frac{n}{6n+9}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2n+3 is 3\left(2n+3\right). Multiply \frac{1}{3} times \frac{2n+3}{2n+3}. Multiply \frac{1}{2n+3} times \frac{3}{3}.

$$\frac{1}{2}\left(\frac{2n+3}{3\left(2n+3\right)}-\frac{3}{3\left(2n+3\right)}\right)$$

Since \frac{2n+3}{3\left(2n+3\right)} and \frac{3}{3\left(2n+3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\times \frac{2n+3-3}{3\left(2n+3\right)}$$

Combine like terms in 2n+3-3.

$$\frac{1}{2}\times \frac{2n}{3\left(2n+3\right)}$$

Multiply \frac{1}{2} times \frac{2n}{3\left(2n+3\right)} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

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

Use the distributive property to multiply 3 by 2n+3.

$$\frac{n}{6n+9}$$