Solve frac{3x^{2}-12}{x^2+4x+4}+x^3-2x^2/x^2+2x

$$\frac { 3 x ^ { 2 } - 12 } { x ^ { 2 } + 4 x + 4 } + \frac { x ^ { 3 } - 2 x ^ { 2 } } { x ^ { 2 } + 2 x }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{2}-12}{x^{2}+4x+4}.

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

Cancel out x+2 in both numerator and denominator.

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

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

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

Cancel out x in both numerator and denominator.

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

Since \frac{3\left(x-2\right)}{x+2} and \frac{x\left(x-2\right)}{x+2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3\left(x-2\right)+x\left(x-2\right).

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

Combine like terms in 3x-6+x^{2}-2x.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{2}-12}{x^{2}+4x+4}.

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

Cancel out x+2 in both numerator and denominator.

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

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

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

Cancel out x in both numerator and denominator.

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

Since \frac{3\left(x-2\right)}{x+2} and \frac{x\left(x-2\right)}{x+2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3\left(x-2\right)+x\left(x-2\right).

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

Combine like terms in 3x-6+x^{2}-2x.

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