If $\alpha, \beta $ are the roots of the equation $ax^2+bx+c=0$, then $\dfrac{\alpha}{a\beta+b}+\dfrac{\beta}{a\alpha+b}$ is equal to

Given ax^2+bx+c=0, alpha+beta = -b/a, alpha*beta = c/a. Expression: (alpha(a*alpha+b) + beta(a*beta+b)) / ((a*beta+b)(a*alpha+b)) = (a*alpha^2 + b*alpha + a*beta^2 + b*beta) / (a^2*alpha*beta + ab(alpha+beta) + b^2). Numerator: a(alpha^2+beta^2) + b(alpha+beta) = a((alpha+beta)^2 - 2*alpha*beta) + b(alpha+beta) = a(b^2/a^2 - 2c/a) - b^2/a = b^2/a - 2c - b^2/a = -2c. Denominator: a^2(c/a) + ab(-b/a) + b^2 = ac - b^2 + b^2 = ac. Result: -2c / ac = -2/a.