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

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

Evaluate

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

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.

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

Apply the distributive property by multiplying each term of a-b by each term of b-a.

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

Combine ab and ba to get 2ab.

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

Expand

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

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.

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

Apply the distributive property by multiplying each term of a-b by each term of b-a.

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

Combine ab and ba to get 2ab.

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