Solve 3/x+1+2/-4+frac{2{x+1}}

$$\frac { \frac { 3 } { x + 1 } + 2 } { - 4 + \frac { 2 } { x + 1 } }$$

Evaluate

$$-\frac{2x+5}{2\left(2x+1\right)}$$

Short Solution Steps

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

$$\frac{\frac{3}{x+1}+\frac{2\left(x+1\right)}{x+1}}{-4+\frac{2}{x+1}}$$

Since \frac{3}{x+1} and \frac{2\left(x+1\right)}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+2\left(x+1\right)}{x+1}}{-4+\frac{2}{x+1}}$$

Do the multiplications in 3+2\left(x+1\right).

$$\frac{\frac{3+2x+2}{x+1}}{-4+\frac{2}{x+1}}$$

Combine like terms in 3+2x+2.

$$\frac{\frac{5+2x}{x+1}}{-4+\frac{2}{x+1}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -4 times \frac{x+1}{x+1}.

$$\frac{\frac{5+2x}{x+1}}{-\frac{4\left(x+1\right)}{x+1}+\frac{2}{x+1}}$$

Since -\frac{4\left(x+1\right)}{x+1} and \frac{2}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+2x}{x+1}}{\frac{-4\left(x+1\right)+2}{x+1}}$$

Do the multiplications in -4\left(x+1\right)+2.

$$\frac{\frac{5+2x}{x+1}}{\frac{-4x-4+2}{x+1}}$$

Combine like terms in -4x-4+2.

$$\frac{\frac{5+2x}{x+1}}{\frac{-4x-2}{x+1}}$$

Divide \frac{5+2x}{x+1} by \frac{-4x-2}{x+1} by multiplying \frac{5+2x}{x+1} by the reciprocal of \frac{-4x-2}{x+1}.

$$\frac{\left(5+2x\right)\left(x+1\right)}{\left(x+1\right)\left(-4x-2\right)}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{2x+5}{-4x-2}$$

Expand

$$-\frac{2x+5}{2\left(2x+1\right)}$$

Short Solution Steps

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

$$\frac{\frac{3}{x+1}+\frac{2\left(x+1\right)}{x+1}}{-4+\frac{2}{x+1}}$$

Since \frac{3}{x+1} and \frac{2\left(x+1\right)}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+2\left(x+1\right)}{x+1}}{-4+\frac{2}{x+1}}$$

Do the multiplications in 3+2\left(x+1\right).

$$\frac{\frac{3+2x+2}{x+1}}{-4+\frac{2}{x+1}}$$

Combine like terms in 3+2x+2.

$$\frac{\frac{5+2x}{x+1}}{-4+\frac{2}{x+1}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -4 times \frac{x+1}{x+1}.

$$\frac{\frac{5+2x}{x+1}}{-\frac{4\left(x+1\right)}{x+1}+\frac{2}{x+1}}$$

Since -\frac{4\left(x+1\right)}{x+1} and \frac{2}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+2x}{x+1}}{\frac{-4\left(x+1\right)+2}{x+1}}$$

Do the multiplications in -4\left(x+1\right)+2.

$$\frac{\frac{5+2x}{x+1}}{\frac{-4x-4+2}{x+1}}$$

Combine like terms in -4x-4+2.

$$\frac{\frac{5+2x}{x+1}}{\frac{-4x-2}{x+1}}$$

Divide \frac{5+2x}{x+1} by \frac{-4x-2}{x+1} by multiplying \frac{5+2x}{x+1} by the reciprocal of \frac{-4x-2}{x+1}.

$$\frac{\left(5+2x\right)\left(x+1\right)}{\left(x+1\right)\left(-4x-2\right)}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{2x+5}{-4x-2}$$