一道含有根号的计算题(字母)计算 (x*√x+x*√y)/(xy-y²)-(x+√xy+y)/(x*√x-y*√y)√是根号,√xy是根号下xy,xy都在根号下面

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 04:52:37
一道含有根号的计算题(字母)计算(x*√x+x*√y)/(xy-y²)-(x+√xy+y)/(x*√x-y*√y)√是根号,√xy是根号下xy,xy都在根号下面一道含有根号的计算题(字母)计

一道含有根号的计算题(字母)计算 (x*√x+x*√y)/(xy-y²)-(x+√xy+y)/(x*√x-y*√y)√是根号,√xy是根号下xy,xy都在根号下面
一道含有根号的计算题(字母)
计算 (x*√x+x*√y)/(xy-y²)-(x+√xy+y)/(x*√x-y*√y)
√是根号,√xy是根号下xy,xy都在根号下面

一道含有根号的计算题(字母)计算 (x*√x+x*√y)/(xy-y²)-(x+√xy+y)/(x*√x-y*√y)√是根号,√xy是根号下xy,xy都在根号下面
设a=√x,b=√y
(x*√x+x*√y)/(xy-y²)-(x+√xy+y)/(x*√x-y*√y)
=(a^3+a^2*b)/(a^2*b^2-b^4)-(a^2+ab+b^2)/(a^3-b^3)
=a^2*(a+b)/(b^2(a-b)(a+b)) - (a^2+ab+b^2)/((a-b)(a^2+ab+b^2))
=a^2/(b^2*(a-b)) - (1/(a-b))
=(1/(b^2*(a-b)))*(a^2-b^2)
=(1/(b^2*(a-b)))*(a+b)(a-b)
=(a+b)/b^2
=(√x+√y)/y

令x^1/2=z,y^1/2=w,
原式=(z^3+z^2w)/(z^2w^2-w^4)-(z^2+zw+w^2)/(z^3-w^3)
=(z^3+z^2w-w^3-w^2z)/(z^2w^2-w^4)
=[(z^3-w^3)+(z^2w-w^2z)]/(z^2w^2-w^4)
=(z^2+2zw+w^2)(z-w)/w^2(z-w)(z+w)
=(z+w)/w^2
=(√x+√y)/y