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

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

Evaluate

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Short Solution Steps

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

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

Since \frac{1}{a} and \frac{b^{-1}a}{a} have the same denominator, subtract them by subtracting their numerators.

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

Combine like terms in 1-b^{-1}a.

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

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

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

Since \frac{1}{b} and \frac{a^{-1}b}{b} have the same denominator, subtract them by subtracting their numerators.

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

Combine like terms in 1-a^{-1}b.

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

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

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

Express \frac{1}{b}a as a single fraction.

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

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

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

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

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

Cancel out b and b.

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

Express \frac{1}{a}b as a single fraction.

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

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

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

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

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

Cancel out a and a.

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

Extract the negative sign in b-a.

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

Cancel out a-b in both numerator and denominator.

$$-1$$

Factor

$$-1$$