Question

if ab/a+b=2 ,ac/a+c=5 , bc/b+c=4 then find a+b+c

Answer 1

Write them in this way, $\frac{1}{a} + \frac{1}{b} = \frac{1}{2}$, $\frac{1}{b} + \frac{1}{c} = \frac{1}{4}$, $\frac{1}{c} + \frac{1}{a} = \frac{1}{5}$. Add them up, $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{2}$(19/20). Then you have, a=40/9, b=40/11, c=-40. Hence, a+b+c=-40(79/99)