Solve 4-12/x+2/2+frac{4{x-3}}

$$\frac { 4 - \frac { 12 } { x + 2 } } { 2 + \frac { 4 } { x - 3 } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x+2}{x+2}.

$$\frac{\frac{4\left(x+2\right)}{x+2}-\frac{12}{x+2}}{2+\frac{4}{x-3}}$$

Since \frac{4\left(x+2\right)}{x+2} and \frac{12}{x+2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4\left(x+2\right)-12}{x+2}}{2+\frac{4}{x-3}}$$

Do the multiplications in 4\left(x+2\right)-12.

$$\frac{\frac{4x+8-12}{x+2}}{2+\frac{4}{x-3}}$$

Combine like terms in 4x+8-12.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x-3}{x-3}.

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

Since \frac{2\left(x-3\right)}{x-3} and \frac{4}{x-3} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\left(x-3\right)+4.

$$\frac{\frac{4x-4}{x+2}}{\frac{2x-6+4}{x-3}}$$

Combine like terms in 2x-6+4.

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

Divide \frac{4x-4}{x+2} by \frac{2x-2}{x-3} by multiplying \frac{4x-4}{x+2} by the reciprocal of \frac{2x-2}{x-3}.

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

Factor the expressions that are not already factored.

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

Cancel out 2\left(x-1\right) in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x+2}{x+2}.

$$\frac{\frac{4\left(x+2\right)}{x+2}-\frac{12}{x+2}}{2+\frac{4}{x-3}}$$

Since \frac{4\left(x+2\right)}{x+2} and \frac{12}{x+2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4\left(x+2\right)-12}{x+2}}{2+\frac{4}{x-3}}$$

Do the multiplications in 4\left(x+2\right)-12.

$$\frac{\frac{4x+8-12}{x+2}}{2+\frac{4}{x-3}}$$

Combine like terms in 4x+8-12.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x-3}{x-3}.

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

Since \frac{2\left(x-3\right)}{x-3} and \frac{4}{x-3} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\left(x-3\right)+4.

$$\frac{\frac{4x-4}{x+2}}{\frac{2x-6+4}{x-3}}$$

Combine like terms in 2x-6+4.

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

Divide \frac{4x-4}{x+2} by \frac{2x-2}{x-3} by multiplying \frac{4x-4}{x+2} by the reciprocal of \frac{2x-2}{x-3}.

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

Factor the expressions that are not already factored.

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

Cancel out 2\left(x-1\right) in both numerator and denominator.

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

Expand the expression.

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