Solve 2/n-h-1/n+2

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

Evaluate

$$\frac{4+3n-hn}{n\left(n+2\right)}$$

Short Solution Steps

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

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

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

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

Do the multiplications in 2\left(n+2\right)-\left(h-1\right)n.

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

Combine like terms in 2n+4-hn+n.

$$\frac{3n+4-hn}{n\left(n+2\right)}$$

Expand n\left(n+2\right).

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

Expand

$$\frac{4+3n-hn}{n\left(n+2\right)}$$

Short Solution Steps

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

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

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

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

Do the multiplications in 2\left(n+2\right)-\left(h-1\right)n.

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

Combine like terms in 2n+4-hn+n.

$$\frac{3n+4-hn}{n\left(n+2\right)}$$

Expand n\left(n+2\right).

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