If \alpha and \beta are the roots of the equation x+a+b=\frac{abx}{ab+ax+bx} then what is (\alpha\beta+\alpha+\beta) equal to?

Explanation

Rearranging x+(a+b) = \frac{abx}{ab+(a+b)x} yields the quadratic equation x^2 + (a+b)x + ab = 0. The sum of the roots \alpha+\beta = -(a+b) and the product \alpha\beta = ab. Therefore, \alpha\beta+\alpha+\beta = ab - a - b.

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