分數問題,有個分數,分子加1=三分之二,分母加1=二分之一,這分數是多少,急!

首先 設分子是x 和 分母是y
方程a: x/y+1=1/2
2x=y 1
2x-1=y ------(1)
把(1)代入方程b
方程b: x+1/y=2/3
x+1/(2x-1)=2/3
3x+3=4x-2
3+2=x
x=5 ----(2)


把(2)代入(1): 2(5)-1=y
10-1=y
y=9
所以這個分數是5/9

個分數是5/9
Hope this can hep you!

2008-07-21 16:30:17 補充：
let x be 分子
let y be 分母
then (x+1)/y = 2/3-------(1)
and
x/(y+1) = 1/2-------------(2)
from (1), 2y = 3x+3, therefore x=(2y-3)/3
put x = (2y-3)/3 into (2)
[(2y-3)/3]/(y+1)=1/2, therefore 2[(2y-3)/3]=y+1, 2(2y-3)=3(y+1)
4y-6=3y+3,
therefore y= 9
also x/(y+1)=1/2=5/10,
therefore x=5