Solve frac{x^{2}-x-6}{2x^2-8x}divx^3-3x^2/x^2-16*1/x+4

$$\frac { x ^ { 2 } - x - 6 } { 2 x ^ { 2 } - 8 x } \div \frac { x ^ { 3 } - 3 x ^ { 2 } } { x ^ { 2 } - 16 } \times \frac { 1 } { x + 4 }$$

Evaluate

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

Short Solution Steps

Divide \frac{x^{2}-x-6}{2x^{2}-8x} by \frac{x^{3}-3x^{2}}{x^{2}-16} by multiplying \frac{x^{2}-x-6}{2x^{2}-8x} by the reciprocal of \frac{x^{3}-3x^{2}}{x^{2}-16}.

$$\frac{\left(x^{2}-x-6\right)\left(x^{2}-16\right)}{\left(2x^{2}-8x\right)\left(x^{3}-3x^{2}\right)}\times \frac{1}{x+4}$$

Factor the expressions that are not already factored in \frac{\left(x^{2}-x-6\right)\left(x^{2}-16\right)}{\left(2x^{2}-8x\right)\left(x^{3}-3x^{2}\right)}.

$$\frac{\left(x-4\right)\left(x-3\right)\left(x+2\right)\left(x+4\right)}{2x\left(x-4\right)\left(x-3\right)x^{2}}\times \frac{1}{x+4}$$

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

$$\frac{\left(x+2\right)\left(x+4\right)}{2xx^{2}}\times \frac{1}{x+4}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\left(x+2\right)\left(x+4\right)}{2x^{3}}\times \frac{1}{x+4}$$

Multiply \frac{\left(x+2\right)\left(x+4\right)}{2x^{3}} times \frac{1}{x+4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+2\right)\left(x+4\right)}{2x^{3}\left(x+4\right)}$$

Cancel out x+4 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Divide \frac{x^{2}-x-6}{2x^{2}-8x} by \frac{x^{3}-3x^{2}}{x^{2}-16} by multiplying \frac{x^{2}-x-6}{2x^{2}-8x} by the reciprocal of \frac{x^{3}-3x^{2}}{x^{2}-16}.

$$\frac{\left(x^{2}-x-6\right)\left(x^{2}-16\right)}{\left(2x^{2}-8x\right)\left(x^{3}-3x^{2}\right)}\times \frac{1}{x+4}$$

Factor the expressions that are not already factored in \frac{\left(x^{2}-x-6\right)\left(x^{2}-16\right)}{\left(2x^{2}-8x\right)\left(x^{3}-3x^{2}\right)}.

$$\frac{\left(x-4\right)\left(x-3\right)\left(x+2\right)\left(x+4\right)}{2x\left(x-4\right)\left(x-3\right)x^{2}}\times \frac{1}{x+4}$$

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

$$\frac{\left(x+2\right)\left(x+4\right)}{2xx^{2}}\times \frac{1}{x+4}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\left(x+2\right)\left(x+4\right)}{2x^{3}}\times \frac{1}{x+4}$$

Multiply \frac{\left(x+2\right)\left(x+4\right)}{2x^{3}} times \frac{1}{x+4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+2\right)\left(x+4\right)}{2x^{3}\left(x+4\right)}$$

Cancel out x+4 in both numerator and denominator.

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