Solve a/b-b/a-a^2+b^2/ab

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

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in aa-bb.

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

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

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

Do the multiplications in a^{2}-b^{2}-\left(a^{2}+b^{2}\right).

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

Combine like terms in a^{2}-b^{2}-a^{2}-b^{2}.

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

Cancel out b in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

Do the multiplications in aa-bb.

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

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

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

Do the multiplications in a^{2}-b^{2}-\left(a^{2}+b^{2}\right).

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

Combine like terms in a^{2}-b^{2}-a^{2}-b^{2}.

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

Cancel out b in both numerator and denominator.

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