Solve x(s)=2+-6s+1/s^2+3s+2

$$x ( s ) = 2 + \frac { - 6 s + 1 } { s ^ { 2 } + 3 s + 2 }$$

Evaluate

$$\frac{2s^{2}+5}{\left(s+1\right)\left(s+2\right)}$$

Short Solution Steps

Factor s^{2}+3s+2.

$$2+\frac{-6s+1}{\left(s+1\right)\left(s+2\right)}$$

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

$$\frac{2\left(s+1\right)\left(s+2\right)}{\left(s+1\right)\left(s+2\right)}+\frac{-6s+1}{\left(s+1\right)\left(s+2\right)}$$

Since \frac{2\left(s+1\right)\left(s+2\right)}{\left(s+1\right)\left(s+2\right)} and \frac{-6s+1}{\left(s+1\right)\left(s+2\right)} have the same denominator, add them by adding their numerators.

$$\frac{2\left(s+1\right)\left(s+2\right)-6s+1}{\left(s+1\right)\left(s+2\right)}$$

Do the multiplications in 2\left(s+1\right)\left(s+2\right)-6s+1.

$$\frac{2s^{2}+4s+2s+4-6s+1}{\left(s+1\right)\left(s+2\right)}$$

Combine like terms in 2s^{2}+4s+2s+4-6s+1.

$$\frac{2s^{2}+5}{\left(s+1\right)\left(s+2\right)}$$

Expand \left(s+1\right)\left(s+2\right).

$$\frac{2s^{2}+5}{s^{2}+3s+2}$$

Expand

$$\frac{2s^{2}+5}{s^{2}+3s+2}$$

Short Solution Steps

Factor s^{2}+3s+2.

$$2+\frac{-6s+1}{\left(s+1\right)\left(s+2\right)}$$

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

$$\frac{2\left(s+1\right)\left(s+2\right)}{\left(s+1\right)\left(s+2\right)}+\frac{-6s+1}{\left(s+1\right)\left(s+2\right)}$$

Since \frac{2\left(s+1\right)\left(s+2\right)}{\left(s+1\right)\left(s+2\right)} and \frac{-6s+1}{\left(s+1\right)\left(s+2\right)} have the same denominator, add them by adding their numerators.

$$\frac{2\left(s+1\right)\left(s+2\right)-6s+1}{\left(s+1\right)\left(s+2\right)}$$

Do the multiplications in 2\left(s+1\right)\left(s+2\right)-6s+1.

$$\frac{2s^{2}+4s+2s+4-6s+1}{\left(s+1\right)\left(s+2\right)}$$

Combine like terms in 2s^{2}+4s+2s+4-6s+1.

$$\frac{2s^{2}+5}{\left(s+1\right)\left(s+2\right)}$$

Expand \left(s+1\right)\left(s+2\right).

$$\frac{2s^{2}+5}{s^{2}+3s+2}$$