Solve 2s^4+3s^3+2s^2+1/s(s^2+2s+2)*(1/2s+1)

$$\frac { 2 s ^ { 4 } + 3 s ^ { 3 } + 2 s ^ { 2 } + 1 } { s ( s ^ { 2 } + 2 s + 2 ) } \times ( \frac { 1 } { 2 s + 1 } )$$

Evaluate

$$\frac{2s^{4}+3s^{3}+2s^{2}+1}{s\left(2s+1\right)\left(s^{2}+2s+2\right)}$$

Short Solution Steps

Use the distributive property to multiply s by s^{2}+2s+2.

$$\frac{2s^{4}+3s^{3}+2s^{2}+1}{s^{3}+2s^{2}+2s}\times \frac{1}{2s+1}$$

Multiply \frac{2s^{4}+3s^{3}+2s^{2}+1}{s^{3}+2s^{2}+2s} times \frac{1}{2s+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2s^{4}+3s^{3}+2s^{2}+1}{\left(s^{3}+2s^{2}+2s\right)\left(2s+1\right)}$$

Use the distributive property to multiply s^{3}+2s^{2}+2s by 2s+1 and combine like terms.

$$\frac{2s^{4}+3s^{3}+2s^{2}+1}{2s^{4}+5s^{3}+6s^{2}+2s}$$

Expand

$$\frac{2s^{4}+3s^{3}+2s^{2}+1}{s\left(2s+1\right)\left(s^{2}+2s+2\right)}$$

Short Solution Steps

Use the distributive property to multiply s by s^{2}+2s+2.

$$\frac{2s^{4}+3s^{3}+2s^{2}+1}{s^{3}+2s^{2}+2s}\times \frac{1}{2s+1}$$

Multiply \frac{2s^{4}+3s^{3}+2s^{2}+1}{s^{3}+2s^{2}+2s} times \frac{1}{2s+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2s^{4}+3s^{3}+2s^{2}+1}{\left(s^{3}+2s^{2}+2s\right)\left(2s+1\right)}$$

Use the distributive property to multiply s^{3}+2s^{2}+2s by 2s+1 and combine like terms.

$$\frac{2s^{4}+3s^{3}+2s^{2}+1}{2s^{4}+5s^{3}+6s^{2}+2s}$$