Solve 4/x+2/x^2/frac{1{2}}

$$\frac{ \frac{ 4 }{ x } + \frac{ 2 }{ { x }^{ 2 } } }{ \frac{ 1 }{ 2 } }$$

Evaluate

$$\frac{4\left(2x+1\right)}{x^{2}}$$

Short Solution Steps

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{4}{x} times \frac{x}{x}.

$$\frac{\frac{4x}{x^{2}}+\frac{2}{x^{2}}}{\frac{1}{2}}$$

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

$$\frac{\frac{4x+2}{x^{2}}}{\frac{1}{2}}$$

Divide \frac{4x+2}{x^{2}} by \frac{1}{2} by multiplying \frac{4x+2}{x^{2}} by the reciprocal of \frac{1}{2}.

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

Use the distributive property to multiply 4x+2 by 2.

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

Expand

$$\frac{4\left(2x+1\right)}{x^{2}}$$

Short Solution Steps

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{4}{x} times \frac{x}{x}.

$$\frac{\frac{4x}{x^{2}}+\frac{2}{x^{2}}}{\frac{1}{2}}$$

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

$$\frac{\frac{4x+2}{x^{2}}}{\frac{1}{2}}$$

Divide \frac{4x+2}{x^{2}} by \frac{1}{2} by multiplying \frac{4x+2}{x^{2}} by the reciprocal of \frac{1}{2}.

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

Use the distributive property to multiply 4x+2 by 2.

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