Solve 1/b^2-1/2b

$$\frac { 1 } { b ^ { 2 } } - \frac { 1 } { 2 b }$$

Evaluate

$$-\frac{1}{2b}+\frac{1}{b^{2}}$$

Solution Steps

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

$$\frac{2}{2b^{2}}-\frac{b}{2b^{2}}$$

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

$$\frac{2-b}{2b^{2}}$$

Factor

$$-\frac{1}{2}\times \left(\frac{1}{b}\right)^{2}\left(b-2\right)$$