Question

解分式方程！！

①
1 2 3
分数线 + 分数线 = 分数线
x-1 x-2 x-3
②
5x 2x-5 7x-10
分数线 + 分数线 = 分数线
x2+x-6 x2-x-12 x2-6x+8
③
1 1 4
分数线 =分数线 - 分数线
x2-x 2x-x2 x2-3x+2

Answer 1

1/(x-1)+2/(x-2)=3/(x-3)
同时乘以(x-1)(x-2)(x-3)
(x-2)(x-3)+2(x-1)(x-3)=3(x-1)(x-2)
x2-5x+6+2x2-8x+6=3x2-9x+6
3x2-13x+12=3x2-9x+6
-13x+9x=6-12
-4x=-6
x=3/2

5x/(x2+x-6)+(2x-5)/(x2-x-12)=(7x-10)/(x2-6x+8)
5x/(x+3)(x-2)+(2x-5)/(x-4)(x+3)=(7x-10)/(x-2)(x-4)
同时乘以(x+3)(x-2)(x-4)
5x(x-4)+(2x-5)(x-2)=(7x-10)(x+3)
5x2-20x+2x2-9x+10=7x2+11x-30
7x2-29x+10=7x2+11x-30
-29x-11x=-30-10
-40x=-40
x=1

1/(x2-x)=1/(2x-x2)-4/(x2-3x+2)
1/x(x-1)=1/x(2-x)-4/(x-1)(x-2)
1/x(x-1)=1/x(2-x)+4/(x-1)(2-x)
同时乘以x(x-1)(2-x)
2-x=x-1+4x
2-x=5x-1
-x-5x=-1-2
-6x=-3
x=1/2

Answer 2

哈哈 这都行啊
这表达法很帅~~~