Solve frac{a^{3}+2a^{2}+a}{a^{2}+6a+9}+sqrt{frac{a^{3}+4a^2+4a}{a^2+6a+9}}-sqrt{a^3/a^2+6a+9}

$$\frac { a ^ { 3 } + 2 a ^ { 2 } + a } { a ^ { 2 } + 6 a + 9 } + \sqrt { \frac { a ^ { 3 } + 4 a ^ { 2 } + 4 a } { a ^ { 2 } + 6 a + 9 } } - \sqrt { \frac { a ^ { 3 } } { a ^ { 2 } + 6 a + 9 } }$$

Evaluate

$$\frac{\sqrt{a}\left(a^{\frac{5}{2}}+2a^{\frac{3}{2}}+2a+\sqrt{a}+6\right)}{\left(a+3\right)^{2}}$$

Differentiate w.r.t. a

$$\frac{a^{\frac{7}{2}}+9a^{\frac{5}{2}}-a^{2}+11a^{\frac{3}{2}}+3\sqrt{a}+9}{\sqrt{a}\left(a+3\right)^{3}}$$