Solve n+f/n-1-n-f/n+1=

$$\frac { n + f } { n - 1 } - \frac { n - f } { n + 1 } =$$

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in n^{2}+n+fn+f-n^{2}+n+fn-f.

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

Expand \left(n-1\right)\left(n+1\right).

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in n^{2}+n+fn+f-n^{2}+n+fn-f.

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

Expand \left(n-1\right)\left(n+1\right).

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