几道分式方程的题解方程:1/(x-1)(X-2)=1/(X-4)(X-5)X/(X-1) -(X-1)/(X-2)=(x
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几道分式方程的题
解方程:1/(x-1)(X-2)=1/(X-4)(X-5)
X/(X-1) -(X-1)/(X-2)=(x-3)/(x-4) - (x-4)/(X-5)
解方程:1/(x-1)(X-2)=1/(X-4)(X-5)
X/(X-1) -(X-1)/(X-2)=(x-3)/(x-4) - (x-4)/(X-5)
第一题 :
1/(x-1)(x-2)=1/(x-4)(x-5)
1/x²-2x-x+2=1/x²-5x-4x+20
1/x²-3x+2=1/x²-9x+20
∵分子相等,∴分母相等
x²-3x+2=x²-9x+20
6x=18
x=3
经检验,x=3是方程的根
第二题:
x/(x-1) -(x-1)/(x-2)=(x-3)/(x-4) - (x-4)/(x-5)
x/x-1 -x-1/x-2=x-3/x-4 -x-4/x-5
x(x-2)(x-4)(x-5)- (x-1)²(x-4)(x-5)/=(x-1)(x-2)(x-3)(x-5)/-(x-1)(x-2)(x-4)²
(x²-2x)(x²-9x+20)-(x²-2x+1)(x²-9x+20)=(x²-3x+2)(x²-8x+15)-(x²-3x+2)(x²-8x+16)
(x^4-11x³+38x²-40x)-(x^4-11x³+39x²-49x+20)=(x^4-11x³+41x²-61x+30)-(x^4-11x³+42x²-64x+32)
x^4-11x³+38x²-40x-x^4+11x³-39x²+49x-20=x^4-11x³+41x²-61x+30-x^4+11x³-42x²+64x-32
-x²+9x-20=3x-x²-2
6x=18
x=3
经检验,x=3是方程的根
1/(x-1)(x-2)=1/(x-4)(x-5)
1/x²-2x-x+2=1/x²-5x-4x+20
1/x²-3x+2=1/x²-9x+20
∵分子相等,∴分母相等
x²-3x+2=x²-9x+20
6x=18
x=3
经检验,x=3是方程的根
第二题:
x/(x-1) -(x-1)/(x-2)=(x-3)/(x-4) - (x-4)/(x-5)
x/x-1 -x-1/x-2=x-3/x-4 -x-4/x-5
x(x-2)(x-4)(x-5)- (x-1)²(x-4)(x-5)/=(x-1)(x-2)(x-3)(x-5)/-(x-1)(x-2)(x-4)²
(x²-2x)(x²-9x+20)-(x²-2x+1)(x²-9x+20)=(x²-3x+2)(x²-8x+15)-(x²-3x+2)(x²-8x+16)
(x^4-11x³+38x²-40x)-(x^4-11x³+39x²-49x+20)=(x^4-11x³+41x²-61x+30)-(x^4-11x³+42x²-64x+32)
x^4-11x³+38x²-40x-x^4+11x³-39x²+49x-20=x^4-11x³+41x²-61x+30-x^4+11x³-42x²+64x-32
-x²+9x-20=3x-x²-2
6x=18
x=3
经检验,x=3是方程的根
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