Each positive rational number can be written in the form: (a^2+b^3)/(c^5+d^7)
where a,b,c,d are positive integers.

I find this fundamentally wrong. Pls explain?

There is no way you can get any possible rational number with very limited values of the expressions ( a^2 + b^3 ) for any positive a or b and ( c^5 + d^7 ) for any positive c or d.

I have tried it for very simple rational numbers there is no solution?