Mistakes give rise to a problem!

Algebra Level 2

If we mistakenly add numerator and denominators, we would think:

\[\Large \dfrac{1}{a} + \dfrac{1}{b}=\dfrac{2}{a+b}.\]

How many ordered pairs \((a.b)\) in the interval \(-10\leq a,b \leq 10\) such that they satisfy the equation above.

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