Solve x+9/x-3-6/x^2-9div6/left(x+3right)^2-3x-3/x-3

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

Evaluate

$$-3$$

Short Solution Steps

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

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

Cancel out 6 in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{\left(x+3\right)^{2}}{x^{2}-9}.

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

Cancel out x+3 in both numerator and denominator.

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

Since \frac{x+9}{x-3} and \frac{x+3}{x-3} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x+9-\left(x+3\right).

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

Combine like terms in x+9-x-3.

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

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

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

Do the multiplications in 6-\left(3x-3\right).

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

Combine like terms in 6-3x+3.

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

Factor the expressions that are not already factored in \frac{9-3x}{x-3}.

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

Extract the negative sign in 3-x.

$$\frac{-3\left(x-3\right)}{x-3}$$

Cancel out x-3 in both numerator and denominator.

$$-3$$

Factor

$$-3$$