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

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

Evaluate

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

Short Solution Steps

To find the opposite of s+1, find the opposite of each term.

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

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

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

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

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

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

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

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

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

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

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

Use the distributive property to multiply s+1 by s^{2}+2s+1 and combine like terms.

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

Expand

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

Short Solution Steps

To find the opposite of s+1, find the opposite of each term.

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

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

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

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

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

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

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

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

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

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

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

Use the distributive property to multiply s+1 by s^{2}+2s+1 and combine like terms.

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