Solve 2x^2-8/x-3*x^2+x-12/x^3+64div2x-4/x^2-4x+6

$$\frac { 2 x ^ { 2 } - 8 } { x - 3 } \times \frac { x ^ { 2 } + x - 12 } { x ^ { 3 } + 64 } \div \frac { 2 x - 4 } { x ^ { 2 } - 4 x + 6 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+x-12}{x^{3}+64}.

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

Cancel out x+4 in both numerator and denominator.

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

Multiply \frac{2x^{2}-8}{x-3} times \frac{x-3}{x^{2}-4x+16} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x-3 in both numerator and denominator.

$$\frac{\frac{2x^{2}-8}{x^{2}-4x+16}}{\frac{2x-4}{x^{2}-4x+6}}$$

Divide \frac{2x^{2}-8}{x^{2}-4x+16} by \frac{2x-4}{x^{2}-4x+6} by multiplying \frac{2x^{2}-8}{x^{2}-4x+16} by the reciprocal of \frac{2x-4}{x^{2}-4x+6}.

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

Factor the expressions that are not already factored.

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

Cancel out 2\left(x-2\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{3}-2x^{2}-2x+12}{x^{2}-4x+16}$$

Expand

$$\frac{x^{3}-2x^{2}-2x+12}{x^{2}-4x+16}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+x-12}{x^{3}+64}.

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

Cancel out x+4 in both numerator and denominator.

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

Multiply \frac{2x^{2}-8}{x-3} times \frac{x-3}{x^{2}-4x+16} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x-3 in both numerator and denominator.

$$\frac{\frac{2x^{2}-8}{x^{2}-4x+16}}{\frac{2x-4}{x^{2}-4x+6}}$$

Divide \frac{2x^{2}-8}{x^{2}-4x+16} by \frac{2x-4}{x^{2}-4x+6} by multiplying \frac{2x^{2}-8}{x^{2}-4x+16} by the reciprocal of \frac{2x-4}{x^{2}-4x+6}.

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

Factor the expressions that are not already factored.

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

Cancel out 2\left(x-2\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{3}-2x^{2}-2x+12}{x^{2}-4x+16}$$