Solve 4x^2/x^2-16(x^3-64/2x)

$$\frac{ 4 { x }^{ 2 } }{ { x }^{ 2 } -16 } ( \frac{ { x }^{ 3 } -64 }{ 2x } )$$

Evaluate

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

Short Solution Steps

Multiply \frac{4x^{2}}{x^{2}-16} times \frac{x^{3}-64}{2x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4x^{2}\left(x^{3}-64\right)}{\left(x^{2}-16\right)\times 2x}$$

Cancel out 2x in both numerator and denominator.

$$\frac{2x\left(x^{3}-64\right)}{x^{2}-16}$$

Factor the expressions that are not already factored.

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

Cancel out x-4 in both numerator and denominator.

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

Expand the expression.

$$\frac{2x^{3}+8x^{2}+32x}{x+4}$$

Expand

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

Short Solution Steps

Multiply \frac{4x^{2}}{x^{2}-16} times \frac{x^{3}-64}{2x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4x^{2}\left(x^{3}-64\right)}{\left(x^{2}-16\right)\times 2x}$$

Cancel out 2x in both numerator and denominator.

$$\frac{2x\left(x^{3}-64\right)}{x^{2}-16}$$

Factor the expressions that are not already factored.

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

Cancel out x-4 in both numerator and denominator.

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

Expand the expression.

$$\frac{2x^{3}+8x^{2}+32x}{x+4}$$