Solve (a-2ab-b^2/a)diva-b/a=

$$( a - \frac { 2 a b - b ^ { 2 } } { a } ) \div \frac { a - b } { a } =$$

Evaluate

$$a-b$$

Short Solution Steps

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

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

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

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

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

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

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

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

Cancel out a in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a-b in both numerator and denominator.

$$a-b$$

Expand

$$a-b$$

Short Solution Steps

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

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

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

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

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

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

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

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

Cancel out a in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a-b in both numerator and denominator.

$$a-b$$