Solve a+2/a-frac{2{a+1}}

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

Evaluate

$$\frac{a+1}{a-1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{a+1}{a+1}.

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

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

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

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

$$\frac{a+2}{\frac{a^{2}+a-2}{a+1}}$$

Divide a+2 by \frac{a^{2}+a-2}{a+1} by multiplying a+2 by the reciprocal of \frac{a^{2}+a-2}{a+1}.

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

Factor the expressions that are not already factored.

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

Cancel out a+2 in both numerator and denominator.

$$\frac{a+1}{a-1}$$

Expand

$$\frac{a+1}{a-1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{a+1}{a+1}.

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

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

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

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

$$\frac{a+2}{\frac{a^{2}+a-2}{a+1}}$$

Divide a+2 by \frac{a^{2}+a-2}{a+1} by multiplying a+2 by the reciprocal of \frac{a^{2}+a-2}{a+1}.

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

Factor the expressions that are not already factored.

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

Cancel out a+2 in both numerator and denominator.

$$\frac{a+1}{a-1}$$