Solve m^2-2m+1/m^2-1div(m-1-m-1/m+1)

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

Evaluate

$$\frac{1}{m}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{m^{2}-2m+1}{m^{2}-1}.

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

Cancel out m-1 in both numerator and denominator.

$$\frac{\frac{m-1}{m+1}}{m-1-\frac{m-1}{m+1}}$$

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

$$\frac{\frac{m-1}{m+1}}{\frac{\left(m-1\right)\left(m+1\right)}{m+1}-\frac{m-1}{m+1}}$$

Since \frac{\left(m-1\right)\left(m+1\right)}{m+1} and \frac{m-1}{m+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{m-1}{m+1}}{\frac{\left(m-1\right)\left(m+1\right)-\left(m-1\right)}{m+1}}$$

Do the multiplications in \left(m-1\right)\left(m+1\right)-\left(m-1\right).

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

Combine like terms in m^{2}+m-m-1-m+1.

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

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

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

Cancel out m+1 in both numerator and denominator.

$$\frac{m-1}{m^{2}-m}$$

Factor the expressions that are not already factored.

$$\frac{m-1}{m\left(m-1\right)}$$

Cancel out m-1 in both numerator and denominator.

$$\frac{1}{m}$$

Expand

$$\frac{1}{m}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{m^{2}-2m+1}{m^{2}-1}.

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

Cancel out m-1 in both numerator and denominator.

$$\frac{\frac{m-1}{m+1}}{m-1-\frac{m-1}{m+1}}$$

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

$$\frac{\frac{m-1}{m+1}}{\frac{\left(m-1\right)\left(m+1\right)}{m+1}-\frac{m-1}{m+1}}$$

Since \frac{\left(m-1\right)\left(m+1\right)}{m+1} and \frac{m-1}{m+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{m-1}{m+1}}{\frac{\left(m-1\right)\left(m+1\right)-\left(m-1\right)}{m+1}}$$

Do the multiplications in \left(m-1\right)\left(m+1\right)-\left(m-1\right).

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

Combine like terms in m^{2}+m-m-1-m+1.

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

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

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

Cancel out m+1 in both numerator and denominator.

$$\frac{m-1}{m^{2}-m}$$

Factor the expressions that are not already factored.

$$\frac{m-1}{m\left(m-1\right)}$$

Cancel out m-1 in both numerator and denominator.

$$\frac{1}{m}$$