Description for Correct answer:
Given equation \( \Large \frac{ \alpha }{x- \alpha }+\frac{ \beta }{x- \beta }=1 \) can be rewritten as \( \Large x^{2}-2 \left( \alpha + \beta \right)x+3 \alpha \beta =0 \)

Let roots be \( \Large \alpha' and\ - \alpha' \)

=> \( \Large \alpha' + \left(- \alpha' \right)=2 \left( \alpha + \beta \right) \)

=> \( \Large 0=2 \left( \alpha + \beta \right) \)

=> \( \Large \alpha + \beta = 0 \)