Question

分式方程，求详细解答过程

Answer 1

[200/(x+3)]+[480/(x-1）]=680/x
[200(x-1)+480(x+3)]/(x+3)(x-1)=680/x
(200x-200+480x+1440)/(x+3)(x-1)=680/x
(680x+1240)/(x+3)(x-1)=680/x
(680x+1240)x=680(x+3)(x-1)
680x^2+1240x=680x^2+1360x-2024
120x=2014
x=17 望采纳

Answer 2

方程两边 同乘以x（x+3）(x-1)，得
200x(x-1)+480x(x+3)=680(x+3)(x-1)
200x2-200x+480x2+1440x=680(x2+2x-3)
680x2+1240x=680x2+1360x-2040
(1360-1240)x=2040
120x=2040
x=17

Answer 3

同乘以x（x+3）(x-1)，则
200x(x-1)+480x(x+3)=680(x+3)(x-1)
200x2-200x+480x2+1440x=680(x2+2x-3)
680x2+1240x=680x2+1360x-2040
(1360-1240)x=2040
120x=2040
x=17

Answer 4

同乘以最简公分母. 即x(x-1)(x+3)
之后就变成整式方程了. 最后需要验根. 没算错的话应该是17.

Answer 5

先通分，得200X﹙X－1﹚ ＋480X﹙X＋3﹚=680﹙X－1﹚﹙X＋3﹚
化简得 200X²－200X＋480X²＋1440X=680﹙X²＋2X－3﹚
X=17

Answer 6

两边同乘以x(x-1)(x+3)展开成二次方程，求解