Solve m^2-2m+1/m^2-1divm-1-m-1/m+1

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

Evaluate

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

Short Solution Steps

Express \frac{\frac{m^{2}-2m+1}{m^{2}-1}}{m} as a single fraction.

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

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

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

Cancel out m-1 in both numerator and denominator.

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

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

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

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

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

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m\left(m+1\right) and m+1 is m\left(m+1\right). Multiply \frac{m-1}{m+1} times \frac{m}{m}.

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

Since \frac{-1-m^{2}}{m\left(m+1\right)} and \frac{\left(m-1\right)m}{m\left(m+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -1-m^{2}-\left(m-1\right)m.

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

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

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

Expand m\left(m+1\right).

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

Expand

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

Short Solution Steps

Express \frac{\frac{m^{2}-2m+1}{m^{2}-1}}{m} as a single fraction.

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

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

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

Cancel out m-1 in both numerator and denominator.

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

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

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

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

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

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m\left(m+1\right) and m+1 is m\left(m+1\right). Multiply \frac{m-1}{m+1} times \frac{m}{m}.

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

Since \frac{-1-m^{2}}{m\left(m+1\right)} and \frac{\left(m-1\right)m}{m\left(m+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -1-m^{2}-\left(m-1\right)m.

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

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

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

Expand m\left(m+1\right).

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