Solve 1/ab-1/a^2/frac{1{a}-2/b}

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of ab and a^{2} is ba^{2}. Multiply \frac{1}{ab} times \frac{a}{a}. Multiply \frac{1}{a^{2}} times \frac{b}{b}.

$$\frac{\frac{a}{ba^{2}}-\frac{b}{ba^{2}}}{\frac{1}{a}-\frac{2}{b}}$$

Since \frac{a}{ba^{2}} and \frac{b}{ba^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{a-b}{ba^{2}}}{\frac{1}{a}-\frac{2}{b}}$$

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{2}{b} times \frac{a}{a}.

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

Since \frac{b}{ab} and \frac{2a}{ab} have the same denominator, subtract them by subtracting their numerators.

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

Divide \frac{a-b}{ba^{2}} by \frac{b-2a}{ab} by multiplying \frac{a-b}{ba^{2}} by the reciprocal of \frac{b-2a}{ab}.

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

Cancel out ab in both numerator and denominator.

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

Use the distributive property to multiply a by -2a+b.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of ab and a^{2} is ba^{2}. Multiply \frac{1}{ab} times \frac{a}{a}. Multiply \frac{1}{a^{2}} times \frac{b}{b}.

$$\frac{\frac{a}{ba^{2}}-\frac{b}{ba^{2}}}{\frac{1}{a}-\frac{2}{b}}$$

Since \frac{a}{ba^{2}} and \frac{b}{ba^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{a-b}{ba^{2}}}{\frac{1}{a}-\frac{2}{b}}$$

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{2}{b} times \frac{a}{a}.

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

Since \frac{b}{ab} and \frac{2a}{ab} have the same denominator, subtract them by subtracting their numerators.

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

Divide \frac{a-b}{ba^{2}} by \frac{b-2a}{ab} by multiplying \frac{a-b}{ba^{2}} by the reciprocal of \frac{b-2a}{ab}.

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

Cancel out ab in both numerator and denominator.

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

Use the distributive property to multiply a by -2a+b.

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