Rút gọn các biểu thức sau: A=1/a-b+1/a+b+2a/a^2+b^2+4a^3/a^4+b^4+8a^7/a^8+b^8
Giải thích
Ta có:1a−b+1a+b=a+b+a−ba−ba+b=2aa2−b2;
2aa2−b2+2aa2+b2=2aa2+b2+a2−b2a2−b2a2+b2=4a3a4−b4;
4a3a4−b4+4a3a4+b4=4a3a4+b4+a4−b4a4−b4a4+b4=8a7a8−b8;
8a7a8−b8+8a7a8+b8=8a7a8+b8+a8−b8a8−b8a8+b8=16a15a16−b16.
Vậy A=16a15a16−b16a≠±b.