1.计算 (x+2)/(x+1)-(x+3)/(x+2)-(x-4)/(x-3)+(x-5)/(x-4)2.解方程2x/(2x-1)+x/(x-2)=23.先化简再求值 求(1/x²-1/y²)[(x²-xy+y²)/(x-y)+(x²+xy+y²)/(x+y)]的值 ,其中x=1/2 y=1/4

1.计算 (x+2)/(x+1)-(x+3)/(x+2)-(x-4)/(x-3)+(x-5)/(x-4)2.解方程2x/(2x-1)+x/(x-2)=23.先化简再求值 求(1/x²-1/y²)[(x²-xy+y²)/(x-y)+(x²+xy+y²)/(x+y)]的值 ,其中x=1/2 y=1/4
1.计算
(x+2)/(x+1)-(x+3)/(x+2)-(x-4)/(x-3)+(x-5)/(x-4)
2.解方程
2x/(2x-1)+x/(x-2)=2
3.先化简再求值 求(1/x²-1/y²)[(x²-xy+y²)/(x-y)+(x²+xy+y²)/(x+y)]的值 ,其中x=1/2 y=1/4

1.计算 (x+2)/(x+1)-(x+3)/(x+2)-(x-4)/(x-3)+(x-5)/(x-4)2.解方程2x/(2x-1)+x/(x-2)=23.先化简再求值 求(1/x²-1/y²)[(x²-xy+y²)/(x-y)+(x²+xy+y²)/(x+y)]的值 ,其中x=1/2 y=1/4
第一个：
(x+2)/(x+1)-(x+3)/(x+2)-(x-4)/(x-3)+(x-5)/(x-4)
=1+1/(x+1) - 1 - 1/(x+2) - 1 +1/(x-3) +1 -1/(x-4)
= (x+2 -x -1)/[(x+1)*(x+2)] +(x-4 -x +3)/[(x-3)*(x-4)]
=1/[(x+1)*(x+2)] +(-1)/[(x-3)*(x-4)]
=[(x-3)*(x-4) - (x+1)*(x+2)] / [(x+1)*(x+2)*(x-3)*(x-4)]
=(10-10x) / [(x+1)*(x+2)*(x-3)*(x-4)]
第二问：
2x/(2x-1)+x/(x-2)=2
1+1/(2x-1) + 1+2/(x-2) = 2
1/(2x-1) + 2/(x-2) =0
1/(2x-1) = -2/(x-2)
2x-1=(-1/2)(x-2)
4x -2 =2 -x
5x=4
x=4/5
第三问：
(1/x²-1/y²) * [(x²-xy+y²)/(x-y)+(x²+xy+y²)/(x+y)]
=(1/x²-1/y²) * {(x+y)*(x²-xy+y²)/[(x-y)*(x+y)] + (x-y)*(x²+xy+y²)/[(x-y)*(x+y)]}
=(1/x²-1/y²) * [ (x³+y³)/(x² - y²) + (x³ -y³)/(x² - y²) ]
=[(1/x +1/y)*(1/x - 1/y) ] *[ (x³+y³)/(x² - y²) + (x³ -y³)/(x² - y²) ]
=[ (y²-x²)/(xy) ] * [ (x³+y³)/(x² - y²) + (x³ -y³)/(x² - y²) ]
=[ (y²-x²)/(xy) ] * 2x³/(x² - y²)
=-2x²/y
代入x=1/2 y=1/4
得到
-2x²/y
=-2 * (1/2)²/(1/4)
=-2 * (1/4) * 4
= -2
所以原式(1/x²-1/y²)[(x²-xy+y²)/(x-y)+(x²+xy+y²)/(x+y)] =-2

1、 (x+2)/(x+1)-(x+3)/(x+2)-(x-4)/(x-3)+(x-5)/(x-4)
=1+1/(x+1)-1-1/(x+2)-1+1/(x-3)+1-1/(x-4)
=1/(x+1)-1/(x+2)+1/(x-3)-1/(x-4)
=1/(x+1)(x+2)-1/(x-3)(x-4)
=[(x^2-7x+12)-(x^2+3x+2)]/(...

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1、 (x+2)/(x+1)-(x+3)/(x+2)-(x-4)/(x-3)+(x-5)/(x-4)
=1+1/(x+1)-1-1/(x+2)-1+1/(x-3)+1-1/(x-4)
=1/(x+1)-1/(x+2)+1/(x-3)-1/(x-4)
=1/(x+1)(x+2)-1/(x-3)(x-4)
=[(x^2-7x+12)-(x^2+3x+2)]/(x+1)(x+2)(x-3)(x-4)
=(-10x+10)/(x+1)(x+2)(x-3)(x-4)
=-10(x-1)/(x+1)(x+2)(x-3)(x-4)
2、（1）(2x-1)^2=9
2x-1=±3
2x=1±3
x=(1±3)/2
即，x=-1或2
（2）(x+1)(x+2)=2x+4
(x+1)(x+2)=2(x+2)
(x+2)(x+1-2)=0
(x-1)(x+2)=0
即，x=1或-2
（3）x^2-x-5=0
根据求根公式，
x=(1-√21)/2或(1+√21)/2
（4）x^2+3x+1=0
根据求根公式，
x=(-3-√5)/2或(-3+√5)/2
3、（x-y)²（x²+xy+y²）² -（x³+y³）（-x³+y³）
=（x³-y³)² +（x³+y³）（x³-y³）
=(x³-y³)(x³-y³+x³+y³)
=2x³(x³-y³)
∴当x=1,y=-1时
原式=2x³(x³-y³)=4

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2. 2x(x-2)/(2x-1)+x=2(x-2)
2x(x-2)+x(2x-1)=2(x-2)(2x-1)
2x*x-4x+2x*x-x=2(2x*x-4x-x+2)
2x*x-4x+2x*x-x=4x*x-8x-2x+4
4x*x-5x=4x*x-10x+4
...

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2. 2x(x-2)/(2x-1)+x=2(x-2)
2x(x-2)+x(2x-1)=2(x-2)(2x-1)
2x*x-4x+2x*x-x=2(2x*x-4x-x+2)
2x*x-4x+2x*x-x=4x*x-8x-2x+4
4x*x-5x=4x*x-10x+4
-5x=-10x+4
5x=4
x=4/5
只会这一问了（x*x是x的平方）

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