Solve n(3/4-1/2n-1/2n+2-3/4)

$$n ( \frac { 3 } { 4 } - \frac { 1 } { 2 n } - \frac { 1 } { 2 n + 2 } - \frac { 3 } { 4 } )$$

Evaluate

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

Short Solution Steps

Subtract \frac{3}{4} from \frac{3}{4} to get 0.

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

Factor 2n+2.

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

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

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

Since -\frac{n+1}{2n\left(n+1\right)} and \frac{n}{2n\left(n+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -\left(n+1\right)-n.

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

Combine like terms in -n-1-n.

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

Express n\times \frac{-2n-1}{2n\left(n+1\right)} as a single fraction.

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

Cancel out n in both numerator and denominator.

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

Use the distributive property to multiply 2 by n+1.

$$\frac{-2n-1}{2n+2}$$

Expand

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

Short Solution Steps

Subtract \frac{3}{4} from \frac{3}{4} to get 0.

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

Factor 2n+2.

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

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

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

Since -\frac{n+1}{2n\left(n+1\right)} and \frac{n}{2n\left(n+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -\left(n+1\right)-n.

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

Combine like terms in -n-1-n.

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

Express n\times \frac{-2n-1}{2n\left(n+1\right)} as a single fraction.

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

Cancel out n in both numerator and denominator.

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

Use the distributive property to multiply 2 by n+1.

$$\frac{-2n-1}{2n+2}$$