Solve 7/s^2+6s+9+2s/s+3

$$\frac { 7 } { s ^ { 2 } + 6 s + 9 } + \frac { 2 s } { s + 3 }$$

Evaluate

$$\frac{2s^{2}+6s+7}{\left(s+3\right)^{2}}$$

Short Solution Steps

Factor s^{2}+6s+9.

$$\frac{7}{\left(s+3\right)^{2}}+\frac{2s}{s+3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(s+3\right)^{2} and s+3 is \left(s+3\right)^{2}. Multiply \frac{2s}{s+3} times \frac{s+3}{s+3}.

$$\frac{7}{\left(s+3\right)^{2}}+\frac{2s\left(s+3\right)}{\left(s+3\right)^{2}}$$

Since \frac{7}{\left(s+3\right)^{2}} and \frac{2s\left(s+3\right)}{\left(s+3\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{7+2s\left(s+3\right)}{\left(s+3\right)^{2}}$$

Do the multiplications in 7+2s\left(s+3\right).

$$\frac{7+2s^{2}+6s}{\left(s+3\right)^{2}}$$

Expand \left(s+3\right)^{2}.

$$\frac{7+2s^{2}+6s}{s^{2}+6s+9}$$

Differentiate w.r.t. s

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