Question

高中数学导学49函数化简结果选择问题3

只有图片一张
最好解析一下

Answer 1

解第一个分式
[x^2+y^(-2)]/[(x^2/3)+y^(-2/3)]
=[(x^2/3)^3+y^(-2/3)^3]/[(x^2/3)+y^(-2/3)]
=[(x^2/3)+y^(-2/3)][(x^4/3)-(x^2/3)y^(-2/3)+y^(-4/3)]/[(x^2/3)+y^(-2/3)]
=(x^4/3)-(x^2/3)y^(-2/3)+y^(-4/3)
同理第二个分式化简为
(x^4/3)+(x^2/3)y^(-2/3)+y^(-4/3)
故原式=-(x^2/3)y^(-2/3)-(x^2/3)y^(-2/3)
=-2(x^2/3)y^(-2/3)
=-2(x^2/3)/y^(2/3)
=-2(x/y)^(2/3)
=-2(开3次)√（x/y）^2
=-2(开3次)√x^2/y^2
=-2(开3次)√x^2y^4/y^2y^4
=-2(开3次)√x^2y^4/y^2
故选A.