Pre-calculus $\frac 27 = \frac 1a + \frac 1b$ I had this questions from a previous exam that I couldn't answer, I am apologizing for any English mistakes or for any stupid questions, I tried to solve them and I searched the internet and I couldn't find answers. 
4-if $\frac 27$ could be written in a unique way in the form of $$\frac 1a +\frac 1b$$ $$a,b \in \mathbb Z^+$$ $$a\neq b$$What is a+b ?
*It seemed so easy maybe I am missing something isn't there infinite values that satisfy this equation?
$7(a+b) = 2ab$
Thanks for taking the time to read the question !

The given problem boils down to finding lattice points on a hyperbola. The equation
$$ 2ab=7(a+b) \tag{1}$$
is equivalent to
$$ (2a-7)(2b-7) = 49\tag{2}$$
and $49=7^2$ cannot be written as a product of integers in too many ways. From the assumption $(2a-7)=1$ and $(2b-7)=49$ we get the non-trivial solution $\color{red}{(a,b)=(4,28)}.$
