Solve 1-3/x+6/x+frac{9{x+6}}

$$\frac { 1 - \frac { 3 } { x + 6 } } { x + \frac { 9 } { x + 6 } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+6}{x+6}.

$$\frac{\frac{x+6}{x+6}-\frac{3}{x+6}}{x+\frac{9}{x+6}}$$

Since \frac{x+6}{x+6} and \frac{3}{x+6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x+6-3}{x+6}}{x+\frac{9}{x+6}}$$

Combine like terms in x+6-3.

$$\frac{\frac{x+3}{x+6}}{x+\frac{9}{x+6}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x+6}{x+6}.

$$\frac{\frac{x+3}{x+6}}{\frac{x\left(x+6\right)}{x+6}+\frac{9}{x+6}}$$

Since \frac{x\left(x+6\right)}{x+6} and \frac{9}{x+6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+3}{x+6}}{\frac{x\left(x+6\right)+9}{x+6}}$$

Do the multiplications in x\left(x+6\right)+9.

$$\frac{\frac{x+3}{x+6}}{\frac{x^{2}+6x+9}{x+6}}$$

Divide \frac{x+3}{x+6} by \frac{x^{2}+6x+9}{x+6} by multiplying \frac{x+3}{x+6} by the reciprocal of \frac{x^{2}+6x+9}{x+6}.

$$\frac{\left(x+3\right)\left(x+6\right)}{\left(x+6\right)\left(x^{2}+6x+9\right)}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{x+3}{x^{2}+6x+9}$$

Factor the expressions that are not already factored.

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

Cancel out x+3 in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+6}{x+6}.

$$\frac{\frac{x+6}{x+6}-\frac{3}{x+6}}{x+\frac{9}{x+6}}$$

Since \frac{x+6}{x+6} and \frac{3}{x+6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x+6-3}{x+6}}{x+\frac{9}{x+6}}$$

Combine like terms in x+6-3.

$$\frac{\frac{x+3}{x+6}}{x+\frac{9}{x+6}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x+6}{x+6}.

$$\frac{\frac{x+3}{x+6}}{\frac{x\left(x+6\right)}{x+6}+\frac{9}{x+6}}$$

Since \frac{x\left(x+6\right)}{x+6} and \frac{9}{x+6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+3}{x+6}}{\frac{x\left(x+6\right)+9}{x+6}}$$

Do the multiplications in x\left(x+6\right)+9.

$$\frac{\frac{x+3}{x+6}}{\frac{x^{2}+6x+9}{x+6}}$$

Divide \frac{x+3}{x+6} by \frac{x^{2}+6x+9}{x+6} by multiplying \frac{x+3}{x+6} by the reciprocal of \frac{x^{2}+6x+9}{x+6}.

$$\frac{\left(x+3\right)\left(x+6\right)}{\left(x+6\right)\left(x^{2}+6x+9\right)}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{x+3}{x^{2}+6x+9}$$

Factor the expressions that are not already factored.

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

Cancel out x+3 in both numerator and denominator.

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