1.若x/3=y/4=z/5,则分式(x+y)/(x-2y+3z)的值.2.若x=y/2=z/5,且x+y+z=4,则x的值.3.已知x=2001,y=2002,则分式(x+y)(x^2+y^2)/(x^4-y^4)的值.4.已知:1/x+1/y=5,求(2x-3xy+2y)/(x+2xy+y)的值.

Question

1.若x/3=y/4=z/5,则分式(x+y)/(x-2y+3z)的值.
2.若x=y/2=z/5,且x+y+z=4,则x的值.
3.已知x=2001,y=2002,则分式(x+y)(x^2+y^2)/(x^4-y^4)的值.
4.已知:1/x+1/y=5,求(2x-3xy+2y)/(x+2xy+y)的值.

Answer 1

1、
令k=x/3=y/4=z/5
则x=3k,y=4k,z=5k
(x+y)/(x-2y+3z)
=(3k+4k)/(3k-8k+15k)
=7k/10k
=7/10
2、
x=y/2=z/5
所以y=2x,z=5x
x+y+z=4
所以x+2x+5x=4
8x=4
x=1/2
3、
(x+y)(x^2+y^2)/(x^4-y^4)
=(x+y)(x^2+y^2)/[(x^2+y^2)(x^2-y^2)]
=(x+y)(x^2+y^2)/[(x^2+y^2)(x+y)(x-y)]
=1/(x-y)
=1/(2001-2002)
=-1
4、
1/x+1/y=5
(x+y)/xy=5
x+y=5xy
(2x-3xy+2y)/(x+2xy+y)
=[2(x+y)-3xy]/[(x+y)+2xy]
=(10xy-3xy)+(5xy+2xy)
=7xy/7xy
=1