Solve (1+1/a-1)diva/a^2-2a+1

$$( 1 + \frac { 1 } { a - 1 } ) \div \frac { a } { a ^ { 2 } - 2 a + 1 }$$

Evaluate

$$a-1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a-1}{a-1}.

$$\frac{\frac{a-1}{a-1}+\frac{1}{a-1}}{\frac{a}{a^{2}-2a+1}}$$

Since \frac{a-1}{a-1} and \frac{1}{a-1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{a-1+1}{a-1}}{\frac{a}{a^{2}-2a+1}}$$

Combine like terms in a-1+1.

$$\frac{\frac{a}{a-1}}{\frac{a}{a^{2}-2a+1}}$$

Divide \frac{a}{a-1} by \frac{a}{a^{2}-2a+1} by multiplying \frac{a}{a-1} by the reciprocal of \frac{a}{a^{2}-2a+1}.

$$\frac{a\left(a^{2}-2a+1\right)}{\left(a-1\right)a}$$

Cancel out a in both numerator and denominator.

$$\frac{a^{2}-2a+1}{a-1}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-1\right)^{2}}{a-1}$$

Cancel out a-1 in both numerator and denominator.

$$a-1$$

Expand

$$a-1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a-1}{a-1}.

$$\frac{\frac{a-1}{a-1}+\frac{1}{a-1}}{\frac{a}{a^{2}-2a+1}}$$

Since \frac{a-1}{a-1} and \frac{1}{a-1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{a-1+1}{a-1}}{\frac{a}{a^{2}-2a+1}}$$

Combine like terms in a-1+1.

$$\frac{\frac{a}{a-1}}{\frac{a}{a^{2}-2a+1}}$$

Divide \frac{a}{a-1} by \frac{a}{a^{2}-2a+1} by multiplying \frac{a}{a-1} by the reciprocal of \frac{a}{a^{2}-2a+1}.

$$\frac{a\left(a^{2}-2a+1\right)}{\left(a-1\right)a}$$

Cancel out a in both numerator and denominator.

$$\frac{a^{2}-2a+1}{a-1}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-1\right)^{2}}{a-1}$$

Cancel out a-1 in both numerator and denominator.

$$a-1$$