Cho a và b là số dương, a ≠ b. Rút gọn biểu thức sau: A= [a-b/ ẩ/4+ a^1/2b^1/4- a^1/2- b^1/2/a^1/4+ b^1/4].

Đặt B=a−ba34+a12b14−a12−b12a14+b14=a−ba12a14+b14−a12−b12a14+b14

=a−b−a12a12−b12a12a14+b14=a−b−a+a12b12a12a14+b14=−b+a12b12a12a14+b14=b12a12−b12a12a14+b14

=b12a14−b14a14+b14a12a14+b14=ba12a14−b14

Do đó A=a−ba34+a12b14−a12−b12a14+b14:a14−b14 =ba12a14−b14:a14−b14

=ba12a14−b14⋅1a14−b14=ba12.