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

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

Evaluate

$$\frac{2\left(x+5\right)}{x+7}$$

Short Solution Steps

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

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

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

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

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

$$\frac{\frac{2+2x+8}{x+4}}{1+\frac{3}{x+4}}$$

Combine like terms in 2+2x+8.

$$\frac{\frac{10+2x}{x+4}}{1+\frac{3}{x+4}}$$

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

$$\frac{\frac{10+2x}{x+4}}{\frac{x+4}{x+4}+\frac{3}{x+4}}$$

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

$$\frac{\frac{10+2x}{x+4}}{\frac{x+4+3}{x+4}}$$

Combine like terms in x+4+3.

$$\frac{\frac{10+2x}{x+4}}{\frac{x+7}{x+4}}$$

Divide \frac{10+2x}{x+4} by \frac{x+7}{x+4} by multiplying \frac{10+2x}{x+4} by the reciprocal of \frac{x+7}{x+4}.

$$\frac{\left(10+2x\right)\left(x+4\right)}{\left(x+4\right)\left(x+7\right)}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{2x+10}{x+7}$$

Expand

$$\frac{2\left(x+5\right)}{x+7}$$

Short Solution Steps

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

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

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

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

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

$$\frac{\frac{2+2x+8}{x+4}}{1+\frac{3}{x+4}}$$

Combine like terms in 2+2x+8.

$$\frac{\frac{10+2x}{x+4}}{1+\frac{3}{x+4}}$$

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

$$\frac{\frac{10+2x}{x+4}}{\frac{x+4}{x+4}+\frac{3}{x+4}}$$

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

$$\frac{\frac{10+2x}{x+4}}{\frac{x+4+3}{x+4}}$$

Combine like terms in x+4+3.

$$\frac{\frac{10+2x}{x+4}}{\frac{x+7}{x+4}}$$

Divide \frac{10+2x}{x+4} by \frac{x+7}{x+4} by multiplying \frac{10+2x}{x+4} by the reciprocal of \frac{x+7}{x+4}.

$$\frac{\left(10+2x\right)\left(x+4\right)}{\left(x+4\right)\left(x+7\right)}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{2x+10}{x+7}$$