Solve (-2s^2+s/s^2+1)-s

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

$$\frac{-2s^{2}+s-s^{3}-s}{s^{2}+1}$$

Combine like terms in -2s^{2}+s-s^{3}-s.

$$\frac{-2s^{2}-s^{3}}{s^{2}+1}$$

Expand

$$-\frac{s^{3}+2s^{2}}{s^{2}+1}$$

Short Solution Steps

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

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

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

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

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

$$\frac{-2s^{2}+s-s^{3}-s}{s^{2}+1}$$

Combine like terms in -2s^{2}+s-s^{3}-s.

$$\frac{-2s^{2}-s^{3}}{s^{2}+1}$$