Solve x/2+2/x-2/frac{2{x}-8/x^2}

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and x is 2x. Multiply \frac{x}{2} times \frac{x}{x}. Multiply \frac{2}{x} times \frac{2}{2}.

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

Since \frac{xx}{2x} and \frac{2\times 2}{2x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in xx+2\times 2.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2x}{2x}.

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

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

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

Do the multiplications in x^{2}+4-2\times 2x.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{2}{x} times \frac{x}{x}.

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

Since \frac{2x}{x^{2}} and \frac{8}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Divide \frac{x^{2}+4-4x}{2x} by \frac{2x-8}{x^{2}} by multiplying \frac{x^{2}+4-4x}{2x} by the reciprocal of \frac{2x-8}{x^{2}}.

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

Cancel out x in both numerator and denominator.

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

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

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

Use the distributive property to multiply 2 by 2x-8.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and x is 2x. Multiply \frac{x}{2} times \frac{x}{x}. Multiply \frac{2}{x} times \frac{2}{2}.

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

Since \frac{xx}{2x} and \frac{2\times 2}{2x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in xx+2\times 2.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2x}{2x}.

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

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

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

Do the multiplications in x^{2}+4-2\times 2x.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{2}{x} times \frac{x}{x}.

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

Since \frac{2x}{x^{2}} and \frac{8}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Divide \frac{x^{2}+4-4x}{2x} by \frac{2x-8}{x^{2}} by multiplying \frac{x^{2}+4-4x}{2x} by the reciprocal of \frac{2x-8}{x^{2}}.

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

Cancel out x in both numerator and denominator.

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

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

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

Use the distributive property to multiply 2 by 2x-8.

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