Question

急，几道分式计算题

要有过程，拜托啦~~！！
分子和分母的最高次项的数为正数 -x²-2x-1/5+4x-3x²
已知1/x-1/y=5,求分式3x+5xy-3y/x-3xy-y的值
已知x+1/x=3,求分式x²+1/x²的值

Answer 1

解答：
（1）(-x^2-2x-1)/(5+4x-3x^2)=(x^2+2x+1)/(3x^2-4x-5)
(2)因为：1/x-1/y=5，得到：y-x=5xy
所以：（3x+5xy-3y）/（x-3xy-y）=[3(x-y)+5xy]/[(x-y)-3xy]
=(-15xy+5xy)/(-8xy)=5/4
(3)x^2+1/x^2=(x+1/x)^2-2=9-2=7

Answer 2

1/x-1/y=5
1/y-1/x=-5

(3x+5xy-3y)/(x-3xy-y)(分子分母同时除以xy)
=(3x/xy+5xy/xy-3y/xy)/(x/xy-3xy/xy-y/xy)
=(3/y+5-3/x)/(1/y-3-1/x)
=(3/y-3/x+5)/(1/y-1/x-3)
=(-5*3+5)/(-5-3)
=-10/(-8)
=5/4

x²+1/x²
=(x+1/x)²-2
=3²-2
=9-2
=7