Solve ab^-1+a^-1/a^-1b

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

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out \frac{1}{a} in both numerator and denominator.

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

Express \frac{1}{b}a^{2} as a single fraction.

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

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

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

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

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

Express \frac{\frac{a^{2}+b}{b}}{b} as a single fraction.

$$\frac{a^{2}+b}{bb}$$

Multiply b and b to get b^{2}.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out \frac{1}{a} in both numerator and denominator.

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

Express \frac{1}{b}a^{2} as a single fraction.

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

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

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

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

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

Express \frac{\frac{a^{2}+b}{b}}{b} as a single fraction.

$$\frac{a^{2}+b}{bb}$$

Multiply b and b to get b^{2}.

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