Solve frac{a^{-2}-a^{-1}*b^-1}{a^-2+a^-1*b^-1}

$$\frac { a ^ { - 2 } - a ^ { - 1 } \cdot b ^ { - 1 } } { a ^ { - 2 } + a ^ { - 1 } \cdot b ^ { - 1 } }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out \left(\frac{1}{a}\right)^{2} in both numerator and denominator.

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

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

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

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

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

Since -\frac{a}{b} and \frac{b}{b} have the same denominator, add them by adding their numerators.

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

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

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

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

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

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

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

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

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

Cancel out b in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out \left(\frac{1}{a}\right)^{2} in both numerator and denominator.

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

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

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

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

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

Since -\frac{a}{b} and \frac{b}{b} have the same denominator, add them by adding their numerators.

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

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

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

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

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

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

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

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

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

Cancel out b in both numerator and denominator.

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