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

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

Evaluate

$$\frac{2-m^{3}}{m\left(m^{2}-1\right)}$$

Short Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

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

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

Since \frac{2}{m^{2}} and \frac{mm^{2}}{m^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2-mm^{2}.

$$\frac{m}{m^{2}-1}\times \frac{2-m^{3}}{m^{2}}$$

Multiply \frac{m}{m^{2}-1} times \frac{2-m^{3}}{m^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{m\left(2-m^{3}\right)}{\left(m^{2}-1\right)m^{2}}$$

Cancel out m in both numerator and denominator.

$$\frac{-m^{3}+2}{m\left(m^{2}-1\right)}$$

Use the distributive property to multiply m by m^{2}-1.

$$\frac{-m^{3}+2}{m^{3}-m}$$

Expand

$$\frac{2-m^{3}}{m\left(m^{2}-1\right)}$$

Short Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

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

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

Since \frac{2}{m^{2}} and \frac{mm^{2}}{m^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2-mm^{2}.

$$\frac{m}{m^{2}-1}\times \frac{2-m^{3}}{m^{2}}$$

Multiply \frac{m}{m^{2}-1} times \frac{2-m^{3}}{m^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{m\left(2-m^{3}\right)}{\left(m^{2}-1\right)m^{2}}$$

Cancel out m in both numerator and denominator.

$$\frac{-m^{3}+2}{m\left(m^{2}-1\right)}$$

Use the distributive property to multiply m by m^{2}-1.

$$\frac{-m^{3}+2}{m^{3}-m}$$