题目

（a的三分之四次方-8乘a的三分之一次方乘b）除以（4乘b的三分之二次方+2乘三次根号下ab）+a的三分之二次方

提问时间：2020-05-08

答案

（a的三分之四次方-8乘a的三分之一次方乘b）除以（4乘b的三分之二次方+2乘三次根号下ab）+a的三分之二次方
=（a^(4/3)-8a^(1/3)b）/（4b^(2/3)+2a^(1/3)b^(1/3)）+a^(2/3)
=a^(1/3)（a-8b）/（2b^(1/3)( 2b^(1/3)+a^(1/3))）+a^(2/3)
=[a^(1/3)/2b^(1/3)]( a^(1/3)+2b^(1/3))(a^(2/3)-2a^(1/3)b^(1/3)+4b^(2/3))/（( a^(1/3)+2b^(1/3))）+a^(2/3)
=[a^(1/3)/2b^(1/3)](a^(2/3)-2a^(1/3)b^(1/3)+4b^(2/3)) +a^(2/3)
=[(a -2a^(2/3)b^(1/3)+4a^(1/3)b^(2/3)]/2b^(1/3) +a^(2/3)
=[(a -2a^(2/3)b^(1/3)+4a^(1/3)b^(2/3) +2a^(2/3)b^(1/3)]/2b^(1/3)
=[(a +4a^(1/3)b^(2/3) ]/2b^(1/3)