Solve 1/2x-1/4x^2+1/8x^3

$$\frac { 1 } { 2 x } - \frac { 1 } { 4 x ^ { 2 } } + \frac { 1 } { 8 x ^ { 3 } }$$

Evaluate

$$\frac{4x^{2}-2x+1}{8x^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x and 4x^{2} is 4x^{2}. Multiply \frac{1}{2x} times \frac{2x}{2x}.

$$\frac{2x}{4x^{2}}-\frac{1}{4x^{2}}+\frac{1}{8x^{3}}$$

Since \frac{2x}{4x^{2}} and \frac{1}{4x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2x-1}{4x^{2}}+\frac{1}{8x^{3}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4x^{2} and 8x^{3} is 8x^{3}. Multiply \frac{2x-1}{4x^{2}} times \frac{2x}{2x}.

$$\frac{\left(2x-1\right)\times 2x}{8x^{3}}+\frac{1}{8x^{3}}$$

Since \frac{\left(2x-1\right)\times 2x}{8x^{3}} and \frac{1}{8x^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\left(2x-1\right)\times 2x+1}{8x^{3}}$$

Do the multiplications in \left(2x-1\right)\times 2x+1.

$$\frac{4x^{2}-2x+1}{8x^{3}}$$

Factor

$$\frac{4x^{2}-2x+1}{8x^{3}}$$