Question is
Are this equal? 1/(a+b) =1/a + 1/b
Does this have a condition for equality?
You can go ahead and add the right side: .
So you are asking for a and b that satisfy
That is the same as .
Solve the quadratic equation .
By the quadratic formula
Since that is not a real number, no, there are no real numbers a and b such that .
$\dfrac{1}{a} + \dfrac{1}{b} = \dfrac{1}{a + b} \implies \dfrac{a + b}{ab} = \dfrac{1}{a + b} \implies a^2 + ab + b^2 = 0 \implies$
$a= \dfrac{- b \pm b\sqrt{-3}}{2} \implies a,\ b \not \in \mathbb R.$
In short, the equality does not apply to any pair of real numbers.