Solve the Rational Equation for positive integer solutions.

I solve this Rational Equation for positive integer solutions

Correction: Sorry, I did not mention in the video that we are solving for POSITIVE integer solutions.

Fortunately I say positive integer solutions in the quiz:

#rationalexpressions
#algebra
#diophontaine equations

[joeanderson]

That’s not the only solution. x and y are both integers, which includes negative numbers. So x can be 12 while y is -156

[HerbertLandei]

When I read about Egyptian fractions, the book mentioned that you can always "prolongate" the representation by splitting 1/n into 1/(n+1) + 1/(n*(n+1)). So this problem was "accidentally" a no-brainer for me.

[mathsplus]

Thanks for another interesting maths solution. I'm learning alot from these interesting problems.