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

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

Evaluate

$$\frac{2\left(3x+2\right)}{\left(2-x\right)\left(x+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x+1}{x+1}.

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

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

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

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

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

Combine like terms in 2x+2+x.

$$\frac{\frac{3x+2}{x+1}}{1-\frac{x}{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

$$\frac{\frac{3x+2}{x+1}}{\frac{2}{2}-\frac{x}{2}}$$

Since \frac{2}{2} and \frac{x}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3x+2}{x+1}}{\frac{2-x}{2}}$$

Divide \frac{3x+2}{x+1} by \frac{2-x}{2} by multiplying \frac{3x+2}{x+1} by the reciprocal of \frac{2-x}{2}.

$$\frac{\left(3x+2\right)\times 2}{\left(x+1\right)\left(2-x\right)}$$

Use the distributive property to multiply 3x+2 by 2.

$$\frac{6x+4}{\left(x+1\right)\left(2-x\right)}$$

Apply the distributive property by multiplying each term of x+1 by each term of 2-x.

$$\frac{6x+4}{2x-x^{2}+2-x}$$

Combine 2x and -x to get x.

$$\frac{6x+4}{x-x^{2}+2}$$

Expand

$$-\frac{2\left(3x+2\right)}{\left(x-2\right)\left(x+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x+1}{x+1}.

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

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

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

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

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

Combine like terms in 2x+2+x.

$$\frac{\frac{3x+2}{x+1}}{1-\frac{x}{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

$$\frac{\frac{3x+2}{x+1}}{\frac{2}{2}-\frac{x}{2}}$$

Since \frac{2}{2} and \frac{x}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3x+2}{x+1}}{\frac{2-x}{2}}$$

Divide \frac{3x+2}{x+1} by \frac{2-x}{2} by multiplying \frac{3x+2}{x+1} by the reciprocal of \frac{2-x}{2}.

$$\frac{\left(3x+2\right)\times 2}{\left(x+1\right)\left(2-x\right)}$$

Use the distributive property to multiply 3x+2 by 2.

$$\frac{6x+4}{\left(x+1\right)\left(2-x\right)}$$

Apply the distributive property by multiplying each term of x+1 by each term of 2-x.

$$\frac{6x+4}{2x-x^{2}+2-x}$$

Combine 2x and -x to get x.

$$\frac{6x+4}{x-x^{2}+2}$$