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

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

Evaluate

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Short Solution Steps

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

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

Since \frac{\left(a+b\right)\left(a-b\right)}{a\left(a-b\right)} and \frac{aa}{a\left(a-b\right)} have the same denominator, subtract them by subtracting their numerators.

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

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

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

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

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

Factor a^{2}-ab.

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

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

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

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

$$\frac{0}{a\left(a-b\right)}$$

Zero divided by any non-zero term gives zero.

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Factor

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