化简和解分式方程化简(x+2)/(x^2-2x) - (x-1)/(x^2-4x+4) /(1-(4/x)解分式方程x/
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/10/04 11:33:14
化简和解分式方程
化简(x+2)/(x^2-2x) - (x-1)/(x^2-4x+4) /(1-(4/x)
解分式方程x/(x-4)=(2x+2)/(x^2-16) +1
化简(x+2)/(x^2-2x) - (x-1)/(x^2-4x+4) /(1-(4/x)
解分式方程x/(x-4)=(2x+2)/(x^2-16) +1
(x+2)/(x^2-2x) - (x-1)/(x^2-4x+4) /(1-(4/x)
=[(x+2)/x(x-2)-(x-1)/(x-2)^2]/[(x-4)/x]
={[(x-2)(x+2)-x(x-1)]/x(x-2)^2}/[(x-4)/x]
=[(x^2-4-x^2+x)/x(x-2)^2}/[(x-4)/x]
=(x-4)/x(x-2)^2}/[(x-4)/x]
=x(x-4)/[x(x-2)^2(x-4)]
=1/(x-2)^2
x/(x-4)=(2x+2)/(x^2-16) +1
x/(x-4)=(2x+2)/(x+4)(x-4)+1
两边乘以(x+4)(x-4)
x(x+4)=2x+2+(x+4)(x-4)
x^2+4x=2x+2+x^2-16
2x=-14
x=-7
经检验,x=-7是方程的解
=[(x+2)/x(x-2)-(x-1)/(x-2)^2]/[(x-4)/x]
={[(x-2)(x+2)-x(x-1)]/x(x-2)^2}/[(x-4)/x]
=[(x^2-4-x^2+x)/x(x-2)^2}/[(x-4)/x]
=(x-4)/x(x-2)^2}/[(x-4)/x]
=x(x-4)/[x(x-2)^2(x-4)]
=1/(x-2)^2
x/(x-4)=(2x+2)/(x^2-16) +1
x/(x-4)=(2x+2)/(x+4)(x-4)+1
两边乘以(x+4)(x-4)
x(x+4)=2x+2+(x+4)(x-4)
x^2+4x=2x+2+x^2-16
2x=-14
x=-7
经检验,x=-7是方程的解
解分式方程:x-1/x+2=x+2/x-1+16/x平方-4
解分式方程:2x+1x
解分式方程:x-3/x-1-x-4/x-2=x-5/x-3-x-6
x-2分之x-x^2-4x+4分之2=1 解分式方程
2x^2-4x-3/x^2-2x-1=3解分式方程
解分式方程3/x-1+4x/1-x^2=-1/x+1
解分式方程(5x-4)/(x-2)=(4x+10)/(3x-6)-1
解分式方程6x-1/3x+2=4x-7/2x-5
解分式方程1/(x-1)(x-2) = 1/(x-4)(x-5)
x/(x-2)+(x+1)/(x-6)=2x/(x-3) 解分式方程
解分式方程:x-2/x+2=x+2/x-2+16/x平方-4
解分式方程:4/5x+x/(5x-25)=5/(x^2-5x)