初二下数学分式方程计算题[ ( x-4 ) / ( x^2 - 1 ) ] ÷ [ ( x^2 - 3x - 4 ) / ( x^2 + 2x + 1 ) ] + (1 / x-1 )其中 x = 2√2 + 1
来源:学生作业帮助网 编辑:作业帮 时间:2024/11/28 05:10:45
初二下数学分式方程计算题[ ( x-4 ) / ( x^2 - 1 ) ] ÷ [ ( x^2 - 3x - 4 ) / ( x^2 + 2x + 1 ) ] + (1 / x-1 )其中 x = 2√2 + 1
初二下数学分式方程计算题
[ ( x-4 ) / ( x^2 - 1 ) ] ÷ [ ( x^2 - 3x - 4 ) / ( x^2 + 2x + 1 ) ] + (1 / x-1 )
其中 x = 2√2 + 1
初二下数学分式方程计算题[ ( x-4 ) / ( x^2 - 1 ) ] ÷ [ ( x^2 - 3x - 4 ) / ( x^2 + 2x + 1 ) ] + (1 / x-1 )其中 x = 2√2 + 1
[ ( x-4 ) / ( x^2 - 1 ) ] ÷ [ ( x^2 - 3x - 4 ) / ( x^2 + 2x + 1 ) ] + (1 / x-1 )
=(x-4)/[(x+1)(x-1)×(x+1)²/[(x-4)(x+1)]+1/(x-1)
=1/(x-1)+1/(x-1)
=2/(x-1)
2/2√2
=√2/2
[ ( x-4 ) / ( x^2 - 1 ) ] ÷ [ ( x^2 - 3x - 4 ) / ( x^2 + 2x + 1 ) ] + 1 /( x-1 )
=[ ( x-4 ) / ( x^2 - 1 ) ] [ ( x^2 + 2x + 1 )/ ( x^2 - 3x - 4 ) ] + 1 /( x-1 )
=[ ( x-4 ) / (x+...
全部展开
[ ( x-4 ) / ( x^2 - 1 ) ] ÷ [ ( x^2 - 3x - 4 ) / ( x^2 + 2x + 1 ) ] + 1 /( x-1 )
=[ ( x-4 ) / ( x^2 - 1 ) ] [ ( x^2 + 2x + 1 )/ ( x^2 - 3x - 4 ) ] + 1 /( x-1 )
=[ ( x-4 ) / (x+ 1 ) (x-1)] [ ( x + 1 )^2/ ( x+1)(x - 4 ) ] + 1 /( x-1 )
=1 /( x-1 )+ 1 /( x-1 )
=2 /( x-1 )
当x = 2√2 + 1时,原式= (√2) /2
收起
√2/2