Question

find the sum. 2a/a^2+6a+9+2/a^2+8a+15

Answer 1

\[2a/a{}^{\wedge}2+6a+9+2/a{}^{\wedge}2+8a+15=24+\frac{2}{a^2}+\frac{2}{a}+14 a \]\[24+\frac{2}{a^2}+\frac{2}{a}+14 a=\left(24+\frac{2}{a^2}\right)+\left(\frac{2}{a}+14 a\right)=\left(\frac{2 \left(1+12 a^2\right)}{a^2}\right)+\left(\frac{2 \left(1+7 a^2\right)}{a}\right) \]\[\left(\frac{2 \left(1+12 a^2\right)}{a^2}\right)+\left(\frac{2 \left(1+7 a^2\right)}{a}\right)=\frac{2 \left(7 a^3+12 a^2+a+1\right)}{a^2} \]