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.

2 11 9 0 8 14 5 1