Solve (x^2+4/x-4)*x^2-4/2x

$$( \frac { x ^ { 2 } + 4 } { x } - 4 ) \cdot \frac { x ^ { 2 } - 4 } { 2 x }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x}{x}.

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

Since \frac{x^{2}+4}{x} and \frac{4x}{x} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Multiply x and x to get x^{2}.

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

Use the distributive property to multiply x^{2}+4-4x by x^{2}-4 and combine like terms.

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

Expand

$$\frac{x^{2}}{2}-2x+\frac{8}{x}-\frac{8}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x}{x}.

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

Since \frac{x^{2}+4}{x} and \frac{4x}{x} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Multiply x and x to get x^{2}.

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

Use the distributive property to multiply x^{2}+4-4x by x^{2}-4 and combine like terms.

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