Solve x^2+9x/x^2+3x-x^2-9/x^2+6x+9

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

Evaluate

$$\frac{12}{x+3}$$

Short Solution Steps

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{x^{2}-9}{x^{2}+6x+9}.

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

Cancel out x+3 in both numerator and denominator.

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

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

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

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

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

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

$$\frac{12}{x+3}$$

Expand

$$\frac{12}{x+3}$$

Short Solution Steps

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{x^{2}-9}{x^{2}+6x+9}.

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

Cancel out x+3 in both numerator and denominator.

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

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

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

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

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

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

$$\frac{12}{x+3}$$