Solve 1/a-1/b/1-frac{1{a}*1/b}

$$\frac { \frac { 1 } { a } - \frac { 1 } { b } } { 1 - \frac { 1 } { a } \cdot \frac { 1 } { b } }$$

Evaluate

$$\frac{b-a}{ab-1}$$

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}.

$$\frac{\frac{b}{ab}-\frac{a}{ab}}{1-\frac{1}{a}\times \frac{1}{b}}$$

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

$$\frac{\frac{b-a}{ab}}{1-\frac{1}{a}\times \frac{1}{b}}$$

Multiply \frac{1}{a} times \frac{1}{b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{b-a}{ab}}{1-\frac{1}{ab}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{ab}{ab}.

$$\frac{\frac{b-a}{ab}}{\frac{ab}{ab}-\frac{1}{ab}}$$

Since \frac{ab}{ab} and \frac{1}{ab} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{b-a}{ab}}{\frac{ab-1}{ab}}$$

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

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

Cancel out ab in both numerator and denominator.

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

Expand

$$\frac{b-a}{ab-1}$$

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}.

$$\frac{\frac{b}{ab}-\frac{a}{ab}}{1-\frac{1}{a}\times \frac{1}{b}}$$

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

$$\frac{\frac{b-a}{ab}}{1-\frac{1}{a}\times \frac{1}{b}}$$

Multiply \frac{1}{a} times \frac{1}{b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{b-a}{ab}}{1-\frac{1}{ab}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{ab}{ab}.

$$\frac{\frac{b-a}{ab}}{\frac{ab}{ab}-\frac{1}{ab}}$$

Since \frac{ab}{ab} and \frac{1}{ab} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{b-a}{ab}}{\frac{ab-1}{ab}}$$

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

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

Cancel out ab in both numerator and denominator.

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