题目

3道简单的分式方程,
1.3/(1-x^) = 2/(1+2x+x) - 5/1-2x+x^
2.5x/(x^+x-6) + (2x-5)/(x^-x-12) = (7x-10)/(x^-6x+8)
3.(x+1)/(x+2) + (x+6)/(x+7) = (x+2)/(x+3) + (x+5)/(x+6)

提问时间：2021-01-07

答案

1.3/(1-x^) = 2/(1+2x+x) - 5/1-2x+x^
3/-（X+1)(X-1)=2/(X+1)^-5/(X-1)^
-3(X+1)(X-1)=2（X-1)^-5（X+1)^
-3X^+3=-3X^-14X-3
X=-6/14
2.5x/(x^+x-6) + (2x-5)/(x^-x-12) = (7x-10)/(x^-6x+8)
5X/(X+3)(X-2)+(2X-5)/(X+3)(X-4)=(7X-10)/(X-2)(X-4)
5X(X-4)+(2X-5)(X-2)=(7X-10)(X+3)
-29X+10=11X-30
X=1
3.(X+1/X+2)-(X+2/X+3)=(X+5/X+6)-(X+6/X+7)
(X方+4X+3-X方-4X-4)/(X方+5X+6)=(X方+12X+35-X方-12X-36)/(X方+13X+42)
X方+5X+6=X方+13X+42
-8X=36
X=-9/2