They are a and b

Algebra Level 4

(a2+1)(b2+1)(a1)(b1)=ab+12\large \frac{{(a}^{2}+1)({b}^{2}+1)}{(a-1)(b-1)} =\frac{ab+1}2

Given that real numbers aa and bb, where a,b1a, b\ne 1, satisfy the equation above. Find a+ba+b.

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