Explanation

(c)
Since, $\alpha$ and $\beta$ are the roots of $x^{2} - ax + a + b = 0$, then
$\alpha + \beta = a$ and $\alpha\beta = a + b$
$\Rightarrow \ \alpha^{2} + \alpha\beta = a\alpha$
$\Rightarrow \ \alpha^{2} - a\alpha = - (a + b)$
And $\alpha\beta + \beta^{2} = a\beta$
$\Rightarrow \ \beta^{2} - a\beta = - (a + b)$
$\therefore\ \frac{1}{\alpha^{2} - a\alpha} + \frac{1}{\beta^{2} - a\beta} + \frac{1}{a + b}$
$= \frac{1}{- (a + b)} + \frac{1}{- (a + b)} + \frac{2}{(a + b)} = 0$