Solve a^2-ab/a^2div(a/b-b/a)

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

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-ab}{a^{2}}.

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

Cancel out a in both numerator and denominator.

$$\frac{\frac{a-b}{a}}{\frac{a}{b}-\frac{b}{a}}$$

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

$$\frac{\frac{a-b}{a}}{\frac{aa}{ab}-\frac{bb}{ab}}$$

Since \frac{aa}{ab} and \frac{bb}{ab} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{a-b}{a}}{\frac{aa-bb}{ab}}$$

Do the multiplications in aa-bb.

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

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

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

Cancel out a in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a-b in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-ab}{a^{2}}.

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

Cancel out a in both numerator and denominator.

$$\frac{\frac{a-b}{a}}{\frac{a}{b}-\frac{b}{a}}$$

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

$$\frac{\frac{a-b}{a}}{\frac{aa}{ab}-\frac{bb}{ab}}$$

Since \frac{aa}{ab} and \frac{bb}{ab} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{a-b}{a}}{\frac{aa-bb}{ab}}$$

Do the multiplications in aa-bb.

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

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

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

Cancel out a in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a-b in both numerator and denominator.

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