m^2+n^2/m^2*n^2= 30
1/n-1/m=5
1/m+1/n=?

 (m²+n²)/(m²*n²)=30⇔m²/(m²*n²) +n²/(m²*n²) =30⇔ 1/n² +1/m² =30⇔
2*(1/n² +1/m²) =60.⇒ (1/n-1/m)² +(1/n+1/m)²  =60 ,но 1/n -1/m =5.
5² +(1/n+1/m)² =60 ;
(1/n+1/m)² =60-25 ;
1/n+1/m =±√35 .