If $$\alpha, \beta$$ are the roots of the equation $$x^2 + 3x - 3$$ , then the value of $$(\alpha + 1)^{-1} + (\beta +1)^{-1}$$ is equal to
$$\frac{1}{\alpha\ +1}+\frac{1}{\beta\ +1}=\frac{\left(\alpha\ +\beta\ +2\right)}{\alpha\ \beta\ +\alpha\ +\beta\ +1}$$
Since $$\alpha\ ,\beta\ $$ are roots of the given equation:
$$\alpha+\beta\ =-3$$
$$\alpha\times\beta\ =-3$$
Then we have: $$\frac{\left(\alpha\ +\beta\ +2\right)}{\alpha\ \beta\ +\alpha\ +\beta\ +1}=\frac{\left(-3+2\right)}{-3-3+1}=\frac{1}{5}$$
Create a FREE account and get: