Solve x^2-4/x*x/2x^2+8div4x-2x^2/x

$$\frac { x ^ { 2 } - 4 } { x } \times \frac { x } { 2 x ^ { 2 } + 8 } \div \frac { 4 x - 2 x ^ { 2 } } { x }$$

Evaluate

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

Short Solution Steps

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{4x-2x^{2}}{x}.

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

Cancel out x in both numerator and denominator.

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

Expand the expression.

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

Express \frac{\frac{x^{2}-4}{2x^{2}+8}}{-2x+4} as a single fraction.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -2+x.

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

Cancel out -x+2 in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{4x-2x^{2}}{x}.

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

Cancel out x in both numerator and denominator.

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

Expand the expression.

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

Express \frac{\frac{x^{2}-4}{2x^{2}+8}}{-2x+4} as a single fraction.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -2+x.

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

Cancel out -x+2 in both numerator and denominator.

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

Expand the expression.

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