化简(x平方-4反之X平方-4X+4+2-X分之X+2)/X分之X-2

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 02:41:15
化简(x平方-4反之X平方-4X+4+2-X分之X+2)/X分之X-2

化简(x平方-4反之X平方-4X+4+2-X分之X+2)/X分之X-2
化简(x平方-4反之X平方-4X+4+2-X分之X+2)/X分之X-2

化简(x平方-4反之X平方-4X+4+2-X分之X+2)/X分之X-2
(一)
{ (x^2-4x+4)/(x^2-4) + (x+2)/(2-x) } ÷ (x-2)/x
= { (x-2)^2/[(x+2)(x-2)] - (x+2)/(x-2) } * x/ (x-2)
= { (x-2)/(x+2) - (x+2)/(x-2) } * x/ (x-2)
= { [ (x-2)^2 - (x+2)^2 ] / [ (x+2)(x-2) ] } * x/ (x-2)
= {-4x / [ (x+2)(x-2) ] } * x/ (x-2)
= -4x^2 / [ (x+2)(x-2)^2 ]
(二)
{ (x^2-4x+4)/(x^2-4) + (x+2)/(2-x) } * (x-2)/x
= { (x-2)^2/[(x+2)(x-2)] - (x+2)/(x-2) } * (x-2)/x
= { (x-2)/(x+2) - (x+2)/(x-2) } * x/ (x-2)
= { [ (x-2)^2 - (x+2)^2 ] / [ (x+2)(x-2) ] } * (x-2)/x
= {-4x / [ (x+2)(x-2) ] } * (x-2)/x
= - 4 / (x+2)