Solve afrac{x^{2}-x-6}{x^2+2x}*x^3+x^2/x^2-2x-3

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

Evaluate

$$ax$$

Short Solution Steps

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

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

Cancel out x+2 in both numerator and denominator.

$$a\times \frac{x-3}{x}\times \frac{x^{3}+x^{2}}{x^{2}-2x-3}$$

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

$$a\times \frac{x-3}{x}\times \frac{\left(x+1\right)x^{2}}{\left(x-3\right)\left(x+1\right)}$$

Cancel out x+1 in both numerator and denominator.

$$a\times \frac{x-3}{x}\times \frac{x^{2}}{x-3}$$

Express a\times \frac{x-3}{x} as a single fraction.

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

Multiply \frac{a\left(x-3\right)}{x} times \frac{x^{2}}{x-3} by multiplying numerator times numerator and denominator times denominator.

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

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

$$ax$$

Expand

$$ax$$

Short Solution Steps

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

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

Cancel out x+2 in both numerator and denominator.

$$a\times \frac{x-3}{x}\times \frac{x^{3}+x^{2}}{x^{2}-2x-3}$$

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

$$a\times \frac{x-3}{x}\times \frac{\left(x+1\right)x^{2}}{\left(x-3\right)\left(x+1\right)}$$

Cancel out x+1 in both numerator and denominator.

$$a\times \frac{x-3}{x}\times \frac{x^{2}}{x-3}$$

Express a\times \frac{x-3}{x} as a single fraction.

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

Multiply \frac{a\left(x-3\right)}{x} times \frac{x^{2}}{x-3} by multiplying numerator times numerator and denominator times denominator.

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

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

$$ax$$