\(a-\frac{1}{a}=\frac{5}{6}\)
Multiply a on both sides:
\(a^2-\frac{5}{6}a-1=0\)
Using the quadratic formula, (\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)) you get two roots. One is positive, one is negative. Use the positive one because a > 0.
That root is \(\boxed{\frac{13}{6}}\)
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