Ta có: $M=\frac{19^{30}+5}{19^{31}+5}$ =>$19M=\frac{19.(19^{30}+5)}{19^{31}+5}$ =>$19M=\frac{19^{31}+95}{19^{31}+5}$ =>$19M=1+\frac{90}{19^{31}+5}$ (1)
Ta có: $N=\frac{19^{31}+5}{19^{32}+5}$ =>$19N=\frac{19.(19^{31}+5)}{19^{32}+5}$ =>$19N=\frac{19^{32}+95}{19^{32}+5}$ =>$19N=1+\frac{90}{19^{32}+5}$ (2)
-Từ (1) và (2) ⇒$1+\frac{90}{19^{31}+5}>$ $1+\frac{90}{19^{32}+5}$ ⇒$M>N$