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

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

Evaluate

$$-\frac{3x+14}{x+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x+4}{x+4}.

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

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

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

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

$$\frac{\frac{2+3x+12}{x+4}}{\frac{2}{x+4}-1}$$

Combine like terms in 2+3x+12.

$$\frac{\frac{14+3x}{x+4}}{\frac{2}{x+4}-1}$$

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

$$\frac{\frac{14+3x}{x+4}}{\frac{2}{x+4}-\frac{x+4}{x+4}}$$

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

$$\frac{\frac{14+3x}{x+4}}{\frac{2-\left(x+4\right)}{x+4}}$$

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

$$\frac{\frac{14+3x}{x+4}}{\frac{2-x-4}{x+4}}$$

Combine like terms in 2-x-4.

$$\frac{\frac{14+3x}{x+4}}{\frac{-2-x}{x+4}}$$

Divide \frac{14+3x}{x+4} by \frac{-2-x}{x+4} by multiplying \frac{14+3x}{x+4} by the reciprocal of \frac{-2-x}{x+4}.

$$\frac{\left(14+3x\right)\left(x+4\right)}{\left(x+4\right)\left(-2-x\right)}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{3x+14}{-x-2}$$

Expand

$$-\frac{3x+14}{x+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x+4}{x+4}.

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

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

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

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

$$\frac{\frac{2+3x+12}{x+4}}{\frac{2}{x+4}-1}$$

Combine like terms in 2+3x+12.

$$\frac{\frac{14+3x}{x+4}}{\frac{2}{x+4}-1}$$

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

$$\frac{\frac{14+3x}{x+4}}{\frac{2}{x+4}-\frac{x+4}{x+4}}$$

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

$$\frac{\frac{14+3x}{x+4}}{\frac{2-\left(x+4\right)}{x+4}}$$

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

$$\frac{\frac{14+3x}{x+4}}{\frac{2-x-4}{x+4}}$$

Combine like terms in 2-x-4.

$$\frac{\frac{14+3x}{x+4}}{\frac{-2-x}{x+4}}$$

Divide \frac{14+3x}{x+4} by \frac{-2-x}{x+4} by multiplying \frac{14+3x}{x+4} by the reciprocal of \frac{-2-x}{x+4}.

$$\frac{\left(14+3x\right)\left(x+4\right)}{\left(x+4\right)\left(-2-x\right)}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{3x+14}{-x-2}$$