Solve {c}{1/2*(8/n-n-6/2)}{*n}

$$\left. \begin{array} { c } { \frac { 1 } { 2 } \times ( \frac { 8 } { n } - \frac { n - 6 } { 2 } ) } \\ { \times n } \end{array} \right.$$

Evaluate

$$-\frac{\left(n-8\right)\left(n+2\right)}{4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of n and 2 is 2n. Multiply \frac{8}{n} times \frac{2}{2}. Multiply \frac{n-6}{2} times \frac{n}{n}.

$$\frac{1}{2}\left(\frac{8\times 2}{2n}-\frac{\left(n-6\right)n}{2n}\right)n$$

Since \frac{8\times 2}{2n} and \frac{\left(n-6\right)n}{2n} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\times \frac{8\times 2-\left(n-6\right)n}{2n}n$$

Do the multiplications in 8\times 2-\left(n-6\right)n.

$$\frac{1}{2}\times \frac{16-n^{2}+6n}{2n}n$$

Multiply \frac{1}{2} times \frac{16-n^{2}+6n}{2n} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16-n^{2}+6n}{2\times 2n}n$$

Express \frac{16-n^{2}+6n}{2\times 2n}n as a single fraction.

$$\frac{\left(16-n^{2}+6n\right)n}{2\times 2n}$$

Cancel out n in both numerator and denominator.

$$\frac{-n^{2}+6n+16}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{-n^{2}+6n+16}{4}$$

Expand

$$-\frac{n^{2}}{4}+\frac{3n}{2}+4$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of n and 2 is 2n. Multiply \frac{8}{n} times \frac{2}{2}. Multiply \frac{n-6}{2} times \frac{n}{n}.

$$\frac{1}{2}\left(\frac{8\times 2}{2n}-\frac{\left(n-6\right)n}{2n}\right)n$$

Since \frac{8\times 2}{2n} and \frac{\left(n-6\right)n}{2n} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\times \frac{8\times 2-\left(n-6\right)n}{2n}n$$

Do the multiplications in 8\times 2-\left(n-6\right)n.

$$\frac{1}{2}\times \frac{16-n^{2}+6n}{2n}n$$

Multiply \frac{1}{2} times \frac{16-n^{2}+6n}{2n} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16-n^{2}+6n}{2\times 2n}n$$

Express \frac{16-n^{2}+6n}{2\times 2n}n as a single fraction.

$$\frac{\left(16-n^{2}+6n\right)n}{2\times 2n}$$

Cancel out n in both numerator and denominator.

$$\frac{-n^{2}+6n+16}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{-n^{2}+6n+16}{4}$$