Bored with Vieta's formulae?

Algebra Level 4

If \(\alpha,\beta\) are the roots of the equation \( x^{2}-p(x+1)-c =0\) (where \(p,c\) are real numbers ,not equal to zero) then \(\large \frac{\alpha^{2}+2\alpha+1}{\alpha^{2}+2\alpha+c} +\frac{\beta^{2}+2\beta+1}{\beta^{2}+2\beta+c} \) is equal to:

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