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

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

Evaluate

$$x^{3}-\frac{8}{x^{3}}$$

Short Solution Steps

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

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

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

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

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

$$\frac{x^{6}-8}{x^{3}}$$

Expand

$$x^{3}-\frac{8}{x^{3}}$$

Short Solution Steps

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

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

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

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

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

$$\frac{x^{6}-8}{x^{3}}$$