Solve 2/x+2+2/frac{12{x+2}-2}

$$\frac { \frac { 2 } { x + 2 } + 2 } { \frac { 12 } { x + 2 } - 2 }$$

Evaluate

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

Short Solution Steps

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

$$\frac{\frac{2}{x+2}+\frac{2\left(x+2\right)}{x+2}}{\frac{12}{x+2}-2}$$

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

$$\frac{\frac{2+2\left(x+2\right)}{x+2}}{\frac{12}{x+2}-2}$$

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

$$\frac{\frac{2+2x+4}{x+2}}{\frac{12}{x+2}-2}$$

Combine like terms in 2+2x+4.

$$\frac{\frac{6+2x}{x+2}}{\frac{12}{x+2}-2}$$

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

$$\frac{\frac{6+2x}{x+2}}{\frac{12}{x+2}-\frac{2\left(x+2\right)}{x+2}}$$

Since \frac{12}{x+2} and \frac{2\left(x+2\right)}{x+2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6+2x}{x+2}}{\frac{12-2\left(x+2\right)}{x+2}}$$

Do the multiplications in 12-2\left(x+2\right).

$$\frac{\frac{6+2x}{x+2}}{\frac{12-2x-4}{x+2}}$$

Combine like terms in 12-2x-4.

$$\frac{\frac{6+2x}{x+2}}{\frac{8-2x}{x+2}}$$

Divide \frac{6+2x}{x+2} by \frac{8-2x}{x+2} by multiplying \frac{6+2x}{x+2} by the reciprocal of \frac{8-2x}{x+2}.

$$\frac{\left(6+2x\right)\left(x+2\right)}{\left(x+2\right)\left(8-2x\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{2x+6}{-2x+8}$$

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

$$\frac{\frac{2}{x+2}+\frac{2\left(x+2\right)}{x+2}}{\frac{12}{x+2}-2}$$

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

$$\frac{\frac{2+2\left(x+2\right)}{x+2}}{\frac{12}{x+2}-2}$$

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

$$\frac{\frac{2+2x+4}{x+2}}{\frac{12}{x+2}-2}$$

Combine like terms in 2+2x+4.

$$\frac{\frac{6+2x}{x+2}}{\frac{12}{x+2}-2}$$

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

$$\frac{\frac{6+2x}{x+2}}{\frac{12}{x+2}-\frac{2\left(x+2\right)}{x+2}}$$

Since \frac{12}{x+2} and \frac{2\left(x+2\right)}{x+2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6+2x}{x+2}}{\frac{12-2\left(x+2\right)}{x+2}}$$

Do the multiplications in 12-2\left(x+2\right).

$$\frac{\frac{6+2x}{x+2}}{\frac{12-2x-4}{x+2}}$$

Combine like terms in 12-2x-4.

$$\frac{\frac{6+2x}{x+2}}{\frac{8-2x}{x+2}}$$

Divide \frac{6+2x}{x+2} by \frac{8-2x}{x+2} by multiplying \frac{6+2x}{x+2} by the reciprocal of \frac{8-2x}{x+2}.

$$\frac{\left(6+2x\right)\left(x+2\right)}{\left(x+2\right)\left(8-2x\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{2x+6}{-2x+8}$$

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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