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> 请阅读某同学解下面分式方程的具体过程.解方程1x-4+4x-1=2x-3+3x-2.1x-4-3x-2=2x-3-4x-1,①-2x+10x2-6x+8=-2x+10x2-4x+3,②1x2-6x+8
请阅读某同学解下面分式方程的具体过程.解方程1x-4+4x-1=2x-3+3x-2.1x-4-3x-2=2x-3-4x-1,①-2x+10x2-6x+8=-2x+10x2-4x+3,②1x2-6x+8
题目简介
请阅读某同学解下面分式方程的具体过程.解方程1x-4+4x-1=2x-3+3x-2.1x-4-3x-2=2x-3-4x-1,①-2x+10x2-6x+8=-2x+10x2-4x+3,②1x2-6x+8
题目详情
请阅读某同学解下面分式方程的具体过程.
解方程
1
x-4
+
4
x-1
=
2
x-3
+
3
x-2
.
1
x-4
-
3
x-2
=
2
x-3
-
4
x-1
,①
-2x+10
x
2
-6x+8
=
-2x+10
x
2
-4x+3
,②
1
x
2
-6x+8
=
1
x
2
-4x+3
,③
∴x
2
-6x+8=x
2
-4x+3.④
∴
x=
5
2
.
把
x=
5
2
代入原方程检验知
x=
5
2
是原方程的解.
上述解答正确吗?如果正确,写出每一步的根据;如果不正确,从哪一步开始出现错误?错误的原因是什么?并给出正确解答.
题型:解答题
难度:中档
来源:不详
答案
class="stub"1
x-4
-
class="stub"3
x-2
=
class="stub"2
x-3
-
class="stub"4
x-1
,①
class="stub"-2x+10
x
2
-6x+8
=
class="stub"-2x+10
x
2
-4x+3
,②
(-2x+10)(x2-4x+3-x2+6x-8)=0,
即(-2x+10)(2x-5)=0,③
∴-2x+10=0,2x-5=0,④
解得x1=5,x2=
class="stub"5
2
,
检验:当x1=5时,(x-4)(x-2)(x-3)(x-1)=(5-4)(5-2)(5-3)(5-1)≠0,
当x2=
class="stub"5
2
时,(x-4)(x-2)(x-3)(x-1)=(
class="stub"5
2
-4)(
class="stub"5
2
-2)(
class="stub"5
2
-3)(
class="stub"5
2
-1)≠0,
所以x1=5,x2=
class="stub"5
2
都是原方程的解,
因此,原分式方程的解是x1=5,x2=
class="stub"5
2
.
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分式方程的解为()A.1B.-1C.-2D.-3-八
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题目简介
请阅读某同学解下面分式方程的具体过程.解方程1x-4+4x-1=2x-3+3x-2.1x-4-3x-2=2x-3-4x-1,①-2x+10x2-6x+8=-2x+10x2-4x+3,②1x2-6x+8
题目详情
解方程
∴x2-6x+8=x2-4x+3.④
∴x=
把x=
上述解答正确吗?如果正确,写出每一步的根据;如果不正确,从哪一步开始出现错误?错误的原因是什么?并给出正确解答.
答案
(-2x+10)(x2-4x+3-x2+6x-8)=0,
即(-2x+10)(2x-5)=0,③
∴-2x+10=0,2x-5=0,④
解得x1=5,x2=
检验:当x1=5时,(x-4)(x-2)(x-3)(x-1)=(5-4)(5-2)(5-3)(5-1)≠0,
当x2=
所以x1=5,x2=
因此,原分式方程的解是x1=5,x2=