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

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

Evaluate

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

Short Solution Steps

Factor ab-b^{2}. Factor a^{2}-ab.

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

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

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

Since \frac{aa}{ab\left(a-b\right)} and \frac{bb}{ab\left(a-b\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in aa+bb.

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

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

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

Since \frac{a^{2}+b^{2}}{ab\left(a-b\right)} and \frac{\left(a+b\right)\left(a-b\right)}{ab\left(a-b\right)} have the same denominator, add them by adding their numerators.

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

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

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

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

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

Cancel out a in both numerator and denominator.

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

Expand b\left(a-b\right).

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

Expand

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

Short Solution Steps

Factor ab-b^{2}. Factor a^{2}-ab.

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

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

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

Since \frac{aa}{ab\left(a-b\right)} and \frac{bb}{ab\left(a-b\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in aa+bb.

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

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

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

Since \frac{a^{2}+b^{2}}{ab\left(a-b\right)} and \frac{\left(a+b\right)\left(a-b\right)}{ab\left(a-b\right)} have the same denominator, add them by adding their numerators.

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

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

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

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

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

Cancel out a in both numerator and denominator.

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

Expand b\left(a-b\right).

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