Solve (1/b-1/a)diva^2-b^2/ab

$$( \frac { 1 } { b } - \frac { 1 } { a } ) \div \frac { a ^ { 2 } - b ^ { 2 } } { a b }$$

Evaluate

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

Short Solution Steps

Divide \frac{1}{b}-\frac{1}{a} by \frac{a^{2}-b^{2}}{ab} by multiplying \frac{1}{b}-\frac{1}{a} by the reciprocal of \frac{a^{2}-b^{2}}{ab}.

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

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

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

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

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

Express \frac{a-b}{ab}a as a single fraction.

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

Cancel out a in both numerator and denominator.

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

Cancel out b and b.

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

Factor the expressions that are not already factored.

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

Cancel out a-b in both numerator and denominator.

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

Expand

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

Short Solution Steps

Divide \frac{1}{b}-\frac{1}{a} by \frac{a^{2}-b^{2}}{ab} by multiplying \frac{1}{b}-\frac{1}{a} by the reciprocal of \frac{a^{2}-b^{2}}{ab}.

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

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

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

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

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

Express \frac{a-b}{ab}a as a single fraction.

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

Cancel out a in both numerator and denominator.

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

Cancel out b and b.

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

Factor the expressions that are not already factored.

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

Cancel out a-b in both numerator and denominator.

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