Solve x-3/x^2+6x+9div(1-6/x+3)

$$\frac { x - 3 } { x ^ { 2 } + 6 x + 9 } \div ( 1 - \frac { 6 } { x + 3 } )$$

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+3}{x+3}.

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

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

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

Combine like terms in x+3-6.

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

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

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

Cancel out x-3 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+3}{x+3}.

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

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

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

Combine like terms in x+3-6.

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

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

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

Cancel out x-3 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.

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