Find-all-rational-solution-of-the-equation-a-b-ab-

Question Number 15788 by tawa tawa last updated on 13/Jun/17

Find all rational solution of the equation a + b = ab

Commented by mrW1 last updated on 14/Jun/17

b = \frac{n}{m}

a + \frac{n}{m} = a \times \frac{n}{m}

(\frac{n}{m} - 1) a = \frac{n}{m}

a = \frac{n}{n - m}

\Rightarrow {\begin{cases} a = \frac{n}{n - m} \\ b = \frac{n}{m} \end{cases}

n, m \in Z \land n \neq m

Commented by tawa tawa last updated on 14/Jun/17

I really appreciate sir . God bless you sir .