一道含有根号的计算题(字母)
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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
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)](/uploads/image/z/17526518-62-8.jpg?t=%E4%B8%80%E9%81%93%E5%90%AB%E6%9C%89%E6%A0%B9%E5%8F%B7%E7%9A%84%E8%AE%A1%E7%AE%97%E9%A2%98%EF%BC%88%E5%AD%97%E6%AF%8D%EF%BC%89)
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
(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