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

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

Evaluate

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

Short Solution Steps

Divide \frac{-4x-x^{2}-4-4x^{2}+4-4x+x^{2}}{x^{2}-4} by \frac{x^{2}-3x}{2x^{2}-x^{3}} by multiplying \frac{-4x-x^{2}-4-4x^{2}+4-4x+x^{2}}{x^{2}-4} by the reciprocal of \frac{x^{2}-3x}{2x^{2}-x^{3}}.

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

Combine -x^{2} and -4x^{2} to get -5x^{2}.

$$\frac{\left(-4x-5x^{2}-4+4-4x+x^{2}\right)\left(2x^{2}-x^{3}\right)}{\left(x^{2}-4\right)\left(x^{2}-3x\right)}$$

Add -4 and 4 to get 0.

$$\frac{\left(-4x-5x^{2}-4x+x^{2}\right)\left(2x^{2}-x^{3}\right)}{\left(x^{2}-4\right)\left(x^{2}-3x\right)}$$

Combine -5x^{2} and x^{2} to get -4x^{2}.

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

Combine -4x and -4x to get -8x.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -2-x. Extract the negative sign in 2-x.

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

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

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

Expand the expression.

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

Expand

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

Short Solution Steps

Divide \frac{-4x-x^{2}-4-4x^{2}+4-4x+x^{2}}{x^{2}-4} by \frac{x^{2}-3x}{2x^{2}-x^{3}} by multiplying \frac{-4x-x^{2}-4-4x^{2}+4-4x+x^{2}}{x^{2}-4} by the reciprocal of \frac{x^{2}-3x}{2x^{2}-x^{3}}.

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

Combine -x^{2} and -4x^{2} to get -5x^{2}.

$$\frac{\left(-4x-5x^{2}-4+4-4x+x^{2}\right)\left(2x^{2}-x^{3}\right)}{\left(x^{2}-4\right)\left(x^{2}-3x\right)}$$

Add -4 and 4 to get 0.

$$\frac{\left(-4x-5x^{2}-4x+x^{2}\right)\left(2x^{2}-x^{3}\right)}{\left(x^{2}-4\right)\left(x^{2}-3x\right)}$$

Combine -5x^{2} and x^{2} to get -4x^{2}.

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

Combine -4x and -4x to get -8x.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -2-x. Extract the negative sign in 2-x.

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

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

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

Expand the expression.

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