Solve 4/b-b/a^2/frac{1{a}-2/b}

$$\frac { \frac { 4 } { b } - \frac { b } { a ^ { 2 } } } { \frac { 1 } { a } - \frac { 2 } { b } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and a^{2} is ba^{2}. Multiply \frac{4}{b} times \frac{a^{2}}{a^{2}}. Multiply \frac{b}{a^{2}} times \frac{b}{b}.

$$\frac{\frac{4a^{2}}{ba^{2}}-\frac{bb}{ba^{2}}}{\frac{1}{a}-\frac{2}{b}}$$

Since \frac{4a^{2}}{ba^{2}} and \frac{bb}{ba^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4a^{2}-bb}{ba^{2}}}{\frac{1}{a}-\frac{2}{b}}$$

Do the multiplications in 4a^{2}-bb.

$$\frac{\frac{4a^{2}-b^{2}}{ba^{2}}}{\frac{1}{a}-\frac{2}{b}}$$

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}.

$$\frac{\frac{4a^{2}-b^{2}}{ba^{2}}}{\frac{b}{ab}-\frac{2a}{ab}}$$

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

$$\frac{\frac{4a^{2}-b^{2}}{ba^{2}}}{\frac{b-2a}{ab}}$$

Divide \frac{4a^{2}-b^{2}}{ba^{2}} by \frac{b-2a}{ab} by multiplying \frac{4a^{2}-b^{2}}{ba^{2}} by the reciprocal of \frac{b-2a}{ab}.

$$\frac{\left(4a^{2}-b^{2}\right)ab}{ba^{2}\left(b-2a\right)}$$

Cancel out ab in both numerator and denominator.

$$\frac{4a^{2}-b^{2}}{a\left(-2a+b\right)}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in 2a-b.

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

Cancel out -2a+b in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and a^{2} is ba^{2}. Multiply \frac{4}{b} times \frac{a^{2}}{a^{2}}. Multiply \frac{b}{a^{2}} times \frac{b}{b}.

$$\frac{\frac{4a^{2}}{ba^{2}}-\frac{bb}{ba^{2}}}{\frac{1}{a}-\frac{2}{b}}$$

Since \frac{4a^{2}}{ba^{2}} and \frac{bb}{ba^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4a^{2}-bb}{ba^{2}}}{\frac{1}{a}-\frac{2}{b}}$$

Do the multiplications in 4a^{2}-bb.

$$\frac{\frac{4a^{2}-b^{2}}{ba^{2}}}{\frac{1}{a}-\frac{2}{b}}$$

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}.

$$\frac{\frac{4a^{2}-b^{2}}{ba^{2}}}{\frac{b}{ab}-\frac{2a}{ab}}$$

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

$$\frac{\frac{4a^{2}-b^{2}}{ba^{2}}}{\frac{b-2a}{ab}}$$

Divide \frac{4a^{2}-b^{2}}{ba^{2}} by \frac{b-2a}{ab} by multiplying \frac{4a^{2}-b^{2}}{ba^{2}} by the reciprocal of \frac{b-2a}{ab}.

$$\frac{\left(4a^{2}-b^{2}\right)ab}{ba^{2}\left(b-2a\right)}$$

Cancel out ab in both numerator and denominator.

$$\frac{4a^{2}-b^{2}}{a\left(-2a+b\right)}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in 2a-b.

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

Cancel out -2a+b in both numerator and denominator.

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

Expand the expression.

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