Solve 1/b+4/2b^2-1

$$\frac { 1 } { b } + \frac { 4 } { 2 b ^ { 2 } } - 1$$

Evaluate

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

Short Solution Steps

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

$$\frac{2b}{2b^{2}}+\frac{4}{2b^{2}}-1$$

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

$$\frac{2b+4}{2b^{2}}-1$$

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

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

Cancel out 2 in both numerator and denominator.

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

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

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

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

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

Factor

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