Solve 5-9/x+4/frac{2x{x+4}-8}

$$\frac { 5 - \frac { 9 } { x + 4 } } { \frac { 2 x } { x + 4 } - 8 }$$

Evaluate

$$-\frac{5x+11}{2\left(3x+16\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{x+4}{x+4}.

$$\frac{\frac{5\left(x+4\right)}{x+4}-\frac{9}{x+4}}{\frac{2x}{x+4}-8}$$

Since \frac{5\left(x+4\right)}{x+4} and \frac{9}{x+4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5\left(x+4\right)-9}{x+4}}{\frac{2x}{x+4}-8}$$

Do the multiplications in 5\left(x+4\right)-9.

$$\frac{\frac{5x+20-9}{x+4}}{\frac{2x}{x+4}-8}$$

Combine like terms in 5x+20-9.

$$\frac{\frac{5x+11}{x+4}}{\frac{2x}{x+4}-8}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 8 times \frac{x+4}{x+4}.

$$\frac{\frac{5x+11}{x+4}}{\frac{2x}{x+4}-\frac{8\left(x+4\right)}{x+4}}$$

Since \frac{2x}{x+4} and \frac{8\left(x+4\right)}{x+4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5x+11}{x+4}}{\frac{2x-8\left(x+4\right)}{x+4}}$$

Do the multiplications in 2x-8\left(x+4\right).

$$\frac{\frac{5x+11}{x+4}}{\frac{2x-8x-32}{x+4}}$$

Combine like terms in 2x-8x-32.

$$\frac{\frac{5x+11}{x+4}}{\frac{-6x-32}{x+4}}$$

Divide \frac{5x+11}{x+4} by \frac{-6x-32}{x+4} by multiplying \frac{5x+11}{x+4} by the reciprocal of \frac{-6x-32}{x+4}.

$$\frac{\left(5x+11\right)\left(x+4\right)}{\left(x+4\right)\left(-6x-32\right)}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{5x+11}{-6x-32}$$

Expand

$$-\frac{5x+11}{2\left(3x+16\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{x+4}{x+4}.

$$\frac{\frac{5\left(x+4\right)}{x+4}-\frac{9}{x+4}}{\frac{2x}{x+4}-8}$$

Since \frac{5\left(x+4\right)}{x+4} and \frac{9}{x+4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5\left(x+4\right)-9}{x+4}}{\frac{2x}{x+4}-8}$$

Do the multiplications in 5\left(x+4\right)-9.

$$\frac{\frac{5x+20-9}{x+4}}{\frac{2x}{x+4}-8}$$

Combine like terms in 5x+20-9.

$$\frac{\frac{5x+11}{x+4}}{\frac{2x}{x+4}-8}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 8 times \frac{x+4}{x+4}.

$$\frac{\frac{5x+11}{x+4}}{\frac{2x}{x+4}-\frac{8\left(x+4\right)}{x+4}}$$

Since \frac{2x}{x+4} and \frac{8\left(x+4\right)}{x+4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5x+11}{x+4}}{\frac{2x-8\left(x+4\right)}{x+4}}$$

Do the multiplications in 2x-8\left(x+4\right).

$$\frac{\frac{5x+11}{x+4}}{\frac{2x-8x-32}{x+4}}$$

Combine like terms in 2x-8x-32.

$$\frac{\frac{5x+11}{x+4}}{\frac{-6x-32}{x+4}}$$

Divide \frac{5x+11}{x+4} by \frac{-6x-32}{x+4} by multiplying \frac{5x+11}{x+4} by the reciprocal of \frac{-6x-32}{x+4}.

$$\frac{\left(5x+11\right)\left(x+4\right)}{\left(x+4\right)\left(-6x-32\right)}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{5x+11}{-6x-32}$$