Solve m/m-1(x-2/m^2-1)-2/m

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x-1 times \frac{m^{2}}{m^{2}}.

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

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

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

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

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

Multiply \frac{m}{m-1} times \frac{xm^{2}-m^{2}-2}{m^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out m in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m\left(m-1\right) and m is m\left(m-1\right). Multiply \frac{2}{m} times \frac{m-1}{m-1}.

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

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

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

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

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

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

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

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

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

Cancel out m in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x-1 times \frac{m^{2}}{m^{2}}.

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

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

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

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

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

Multiply \frac{m}{m-1} times \frac{xm^{2}-m^{2}-2}{m^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out m in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m\left(m-1\right) and m is m\left(m-1\right). Multiply \frac{2}{m} times \frac{m-1}{m-1}.

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

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

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

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

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

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

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

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

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

Cancel out m in both numerator and denominator.

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