Solve 1-4/x+8/x+frac{16{x+8}}

$$\frac { 1 - \frac { 4 } { x + 8 } } { x + \frac { 16 } { x + 8 } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+8}{x+8}.

$$\frac{\frac{x+8}{x+8}-\frac{4}{x+8}}{x+\frac{16}{x+8}}$$

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

$$\frac{\frac{x+8-4}{x+8}}{x+\frac{16}{x+8}}$$

Combine like terms in x+8-4.

$$\frac{\frac{x+4}{x+8}}{x+\frac{16}{x+8}}$$

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

$$\frac{\frac{x+4}{x+8}}{\frac{x\left(x+8\right)}{x+8}+\frac{16}{x+8}}$$

Since \frac{x\left(x+8\right)}{x+8} and \frac{16}{x+8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+4}{x+8}}{\frac{x\left(x+8\right)+16}{x+8}}$$

Do the multiplications in x\left(x+8\right)+16.

$$\frac{\frac{x+4}{x+8}}{\frac{x^{2}+8x+16}{x+8}}$$

Divide \frac{x+4}{x+8} by \frac{x^{2}+8x+16}{x+8} by multiplying \frac{x+4}{x+8} by the reciprocal of \frac{x^{2}+8x+16}{x+8}.

$$\frac{\left(x+4\right)\left(x+8\right)}{\left(x+8\right)\left(x^{2}+8x+16\right)}$$

Cancel out x+8 in both numerator and denominator.

$$\frac{x+4}{x^{2}+8x+16}$$

Factor the expressions that are not already factored.

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

Cancel out x+4 in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+8}{x+8}.

$$\frac{\frac{x+8}{x+8}-\frac{4}{x+8}}{x+\frac{16}{x+8}}$$

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

$$\frac{\frac{x+8-4}{x+8}}{x+\frac{16}{x+8}}$$

Combine like terms in x+8-4.

$$\frac{\frac{x+4}{x+8}}{x+\frac{16}{x+8}}$$

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

$$\frac{\frac{x+4}{x+8}}{\frac{x\left(x+8\right)}{x+8}+\frac{16}{x+8}}$$

Since \frac{x\left(x+8\right)}{x+8} and \frac{16}{x+8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+4}{x+8}}{\frac{x\left(x+8\right)+16}{x+8}}$$

Do the multiplications in x\left(x+8\right)+16.

$$\frac{\frac{x+4}{x+8}}{\frac{x^{2}+8x+16}{x+8}}$$

Divide \frac{x+4}{x+8} by \frac{x^{2}+8x+16}{x+8} by multiplying \frac{x+4}{x+8} by the reciprocal of \frac{x^{2}+8x+16}{x+8}.

$$\frac{\left(x+4\right)\left(x+8\right)}{\left(x+8\right)\left(x^{2}+8x+16\right)}$$

Cancel out x+8 in both numerator and denominator.

$$\frac{x+4}{x^{2}+8x+16}$$

Factor the expressions that are not already factored.

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

Cancel out x+4 in both numerator and denominator.

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