Solve a/b-2+b/a

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{b}{b}.

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

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

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

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

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

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

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

Do the multiplications in \left(a-2b\right)a+bb.

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

Factor

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