Answer
$\dfrac{2}{a+2}+\dfrac{1}{a}+\dfrac{a-1}{a^{2}+2a}=\dfrac{4a+1}{a(a+2)}$
Work Step by Step
$\dfrac{2}{a+2}+\dfrac{1}{a}+\dfrac{a-1}{a^{2}+2a}$
Take out common factor $a$ from the denominator of the third fraction:
$\dfrac{2}{a+2}+\dfrac{1}{a}+\dfrac{a-1}{a^{2}+2a}=...$
$...=\dfrac{2}{a+2}+\dfrac{1}{a}+\dfrac{a-1}{a(a+2)}=...$
Evaluate the sum of the three rational expressions by using the LCD, which is $a(a+2)$ in this case:
$...=\dfrac{2a+a+2+a-1}{a(a+2)}=...$
Simplify:
$...=\dfrac{4a+1}{a(a+2)}$
