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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

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

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

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

Expand the expression.

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