Solve frac{x^{3}+3x^{2}}{x^3-6x^2-40x}*x^2-16/x^2-x-12

$$\frac { x ^ { 3 } + 3 x ^ { 2 } } { x ^ { 3 } - 6 x ^ { 2 } - 40 x } \cdot \frac { x ^ { 2 } - 16 } { x ^ { 2 } - x - 12 }$$

Evaluate

$$\frac{x}{x-10}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{3}+3x^{2}}{x^{3}-6x^{2}-40x}.

$$\frac{\left(x+3\right)x^{2}}{x\left(x-10\right)\left(x+4\right)}\times \frac{x^{2}-16}{x^{2}-x-12}$$

Cancel out x in both numerator and denominator.

$$\frac{x\left(x+3\right)}{\left(x-10\right)\left(x+4\right)}\times \frac{x^{2}-16}{x^{2}-x-12}$$

Factor the expressions that are not already factored in \frac{x^{2}-16}{x^{2}-x-12}.

$$\frac{x\left(x+3\right)}{\left(x-10\right)\left(x+4\right)}\times \frac{\left(x-4\right)\left(x+4\right)}{\left(x-4\right)\left(x+3\right)}$$

Cancel out x-4 in both numerator and denominator.

$$\frac{x\left(x+3\right)}{\left(x-10\right)\left(x+4\right)}\times \frac{x+4}{x+3}$$

Multiply \frac{x\left(x+3\right)}{\left(x-10\right)\left(x+4\right)} times \frac{x+4}{x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x\left(x+3\right)\left(x+4\right)}{\left(x-10\right)\left(x+4\right)\left(x+3\right)}$$

Cancel out \left(x+3\right)\left(x+4\right) in both numerator and denominator.

$$\frac{x}{x-10}$$

Expand

$$\frac{x}{x-10}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{3}+3x^{2}}{x^{3}-6x^{2}-40x}.

$$\frac{\left(x+3\right)x^{2}}{x\left(x-10\right)\left(x+4\right)}\times \frac{x^{2}-16}{x^{2}-x-12}$$

Cancel out x in both numerator and denominator.

$$\frac{x\left(x+3\right)}{\left(x-10\right)\left(x+4\right)}\times \frac{x^{2}-16}{x^{2}-x-12}$$

Factor the expressions that are not already factored in \frac{x^{2}-16}{x^{2}-x-12}.

$$\frac{x\left(x+3\right)}{\left(x-10\right)\left(x+4\right)}\times \frac{\left(x-4\right)\left(x+4\right)}{\left(x-4\right)\left(x+3\right)}$$

Cancel out x-4 in both numerator and denominator.

$$\frac{x\left(x+3\right)}{\left(x-10\right)\left(x+4\right)}\times \frac{x+4}{x+3}$$

Multiply \frac{x\left(x+3\right)}{\left(x-10\right)\left(x+4\right)} times \frac{x+4}{x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x\left(x+3\right)\left(x+4\right)}{\left(x-10\right)\left(x+4\right)\left(x+3\right)}$$

Cancel out \left(x+3\right)\left(x+4\right) in both numerator and denominator.

$$\frac{x}{x-10}$$