Solve (a+b)*(1/a-1/b)

$$( a + b ) \cdot ( \frac { 1 } { a } - \frac { 1 } { b } )$$

Evaluate

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

Short Solution Steps

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

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

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

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

Express \left(a+b\right)\times \frac{b-a}{ab} as a single fraction.

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

Consider \left(a+b\right)\left(b-a\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Expand

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

Short Solution Steps

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

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

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

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

Express \left(a+b\right)\times \frac{b-a}{ab} as a single fraction.

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

Consider \left(a+b\right)\left(b-a\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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