Solve a^2-b^2/bdiv(a^2/b-a)

$$\frac { a ^ { 2 } - b ^ { 2 } } { b } \div ( \frac { a ^ { 2 } } { b } - a )$$

Evaluate

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

Short Solution Steps

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

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

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

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

Divide \frac{a^{2}-b^{2}}{b} by \frac{a^{2}-ab}{b} by multiplying \frac{a^{2}-b^{2}}{b} by the reciprocal of \frac{a^{2}-ab}{b}.

$$\frac{\left(a^{2}-b^{2}\right)b}{b\left(a^{2}-ab\right)}$$

Cancel out b in both numerator and denominator.

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

Factor the expressions that are not already factored.

$$\frac{\left(a+b\right)\left(a-b\right)}{a\left(a-b\right)}$$

Cancel out a-b in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

Divide \frac{a^{2}-b^{2}}{b} by \frac{a^{2}-ab}{b} by multiplying \frac{a^{2}-b^{2}}{b} by the reciprocal of \frac{a^{2}-ab}{b}.

$$\frac{\left(a^{2}-b^{2}\right)b}{b\left(a^{2}-ab\right)}$$

Cancel out b in both numerator and denominator.

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

Factor the expressions that are not already factored.

$$\frac{\left(a+b\right)\left(a-b\right)}{a\left(a-b\right)}$$

Cancel out a-b in both numerator and denominator.

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