Question

求解一道初中数学题，要详细过程，不要跳步

Answer 1

解：
(5X+4) / (X-2) = [ (4X+10) / (3X-6) ] -1
(5X+4) / (X-2) =(4X+10) / (3X-6) -(3X-6) / (3X-6)

(5X+4) / (X-2) =[ (4X+10) - (3X-6) ] / (3X-6)

(5X+4) / (X-2) =(4X-3X+10+6) / (3X-6)

(5X+4) / (X-2) =(X+16) / (3X-6)
根据原 理，得：
（5X+4) (3X-6) = (X-2) (X+16)
15X^2-30X+12X-24=X^2+16X-2X-32
15^2-X^2-30X-16X+2X+12X-24+32 = 0
14X^2-32X+8 =0
7X^2-16X+4 = 0
(7X-2) (X-2) = 0
解得：X1 = 2 / 7 X2 = 2
从题中看因为分母(x-2)不能为0 故 X2 = 2 设去。
故原题解为：X = 2/7 (即 X 值为 七分之二）

Answer 2

(5x+4)/(x-2)=(4x+10)/(3x-6)-1
(5x+4)/(x-2)*(x-2)=[(4x+10)/(3x-6)-1]*(x-2)
5x+4=(4x+10)/3-(x-2)
5x+4=4x/3+10/3-x+2
5x=4x/3+10/3-x+2-4
5x+x-4x/3=4/3
(5x+x-4x/3)*3=(4/3)*3
15x+3x-4x=4
14x=4
x=4/14
x=2/7

验算：
(5x+4)/(x-2)=(4x+10)/(3x-6)-1
(5*2/7+4)/(2/7-2)=(4*2/7+10)/(3*2/7-6)-1
(38/7)/(-12/7)=(78/7)/(-36/7)-1
(38/7)*(-7/12)=(78/7)*(-7/36)-1
-(19/6)=(-13/6)-1
-(19/6)=-(19/6)

很完整了

Answer 3

5x+4/x-2  =4x+10/3x-6 -1

5x+4/x-2  =4x+10/3x-6-(3x-6/3x-6)

5x+4/x-2  =(4x+10-3x+6)/3x-6

5x+4/x-2  =x+16/3x-6

• 等号左边分数上下同×3 就得

15x+12/3x-6 =x+16/3x-6

• 去分母

15x+12 =x+16       解得x=7/2              忘满意

Answer 4

两边同乘以共分母（x-2)(3x-6)

5x+4/x-2  =4x+10/3x-6 -1

5x+4/x-2  =4x+10/3x-6-(3x-6/3x-6)

5x+4/x-2  =(4x+10-3x+6)/3x-6

5x+4/x-2  =x+16/3x-6

• 等号左边分数上下同×3 就得

15x+12/3x-6 =x+16/3x-6

• 去分母

15x+12 =x+16       解得x=7/2         

Answer 5

5X+4/(X-2)=(4X+10)/(3X-6)-1
解：(5X+4)/(X-2)=(4X+10-3X+6)/(3X-6)
(5X+4)/(X-2)=(X+16)/(3X-6)
3*(5X+4)=X+16
14X=4
X=2/7
经检验：x=2/7是原方程的解