题目如下：
[(x+2)/(x^2-2x)-(x-1)/(x^2-4x+4)] / [(x-4)/x]
[(m^2-n^2)/(m-n)^2] * [(n-m)/(mn)]^2 / [(m+n)/m]
[(x^2-y^2)/(xy)]^2 / (x+y) * [x/(x-y)]^3
[(x^2+4x+4)/(x^2+2x+1)] / [(x+2)/2]^2 * (x^2+x)
这些题目为式的化简,需要合并同类项、通分、约分等计算法则的混合应用.
希望如下的解答过程能够帮助你解决这些题目.
[(x+2)/(x^2-2x)-(x-1)/(x^2-4x+4)] / [(x-4)/x]
=[(x+2)/(x^2-2x)-(x-1)/(x^2-4x+4)] * [x/(x-4)]
=[(x+2)/(x^2-2x)]*[x/(x-4)]-[(x-1)/(x^2-4x+4)]*[x/(x-4)]
=(x+2)/[x(x-2)] * [x/(x-4)]-(x-1)/(x-2)^2 * [x/(x-4)]
=(x+2)/[(x-2)(x-4)]-[x(x-1)]/[(x-2)^2 (x-4)]
=[(x+2)(x-2)-x(x-1)]/[(x-2)^2 (x-4)]
=(x^2-4-x^2+x)/[(x-2)^2 (x-4)]
=(x-4)/[(x-2)^2 (x-4)]
=1/(x-2)^2
[(m^2-n^2)/(m-n)^2] * [(n-m)/(mn)]^2 / [(m+n)/m]
=[(m^2-n^2)/(m-n)^2] * [(n-m)/(mn)]^2 * [m/(m+n)]
=[(m+n)(m-n)/(m-n)^2] * [(n-m)^2/(m^2n^2)] * [m/(m+n)]
=[(m+n)(m-n)/(m-n)^2] * [(m-n)^2/(m^2n^2)] * [m/(m+n)]
=[m(m+n)(m-n)(m-n)^2] / (m+n)(m^2n^2)(m-n)^2
=(m-n)/(mn^2)
[(x^2-y^2)/(xy)]^2 / (x+y) * [x/(x-y)]^3
=[(x^2-y^2)/(xy)]^2 * [1/(x+y)] * [x/(x-y)]^3
=[(x+y)(x-y)/(xy)]^2 * [1/(x+y)] * [x/(x-y)]^3
=[(x+y)^2 (x-y)^2/(x^2y^2)] * [1/(x+y)] * [x^3/(x-y)^3]
=[(x+y)^2 (x-y)^2 x^3] / [(x^2y^2)(x+y)(x-y)^3]
=[x(x+y)] / [(x-y)y^2]
[(x^2+4x+4)/(x^2+2x+1)] / [(x+2)/2]^2 * (x^2+x)
=[(x^2+4x+4)/(x^2+2x+1)] / [(x+2)^2/2^2] * (x^2+x)
=[(x^2+4x+4)/(x^2+2x+1)] * [4/(x+2)^2] * (x^2+x)
=[(x+2)^2 / (x+1)^2] * [4/(x+2)^2] * [x(x+1)]
=[4x(x+1)(x+2)^2 ] / [(x+1)^2 * (x+2)^2]
=4x / (x+1)
题目的解答过程如上,希望你能理解解答过程从而帮助你解决这些题目.
望能给予采纳!
