Question

(a-1/a的平方-4a+4

化简求值：[(a-1/a的平方-4a+4)-(a+2/a的平方-2a)]÷[4/a-1] a=2—根号3

Answer 1

原式=[(a-1)/(a²-4a+4)-(a+2)/(a²-2a)]÷[4/(a-1)]
={ (a-1)/(a-2)²-(a+2)/[a(a-2)] }×[(a-1)/4]
={ a(a-1)/[a(a-2)²]-(a+2)(a-2)/[a(a-2)²] }×[(a-1)/4]
={ [a(a-1)-(a+2)(a-2)]/[a(a-2)²] }×[(a-1)/4]
={ (a²-a-a²+4)/[a(a-2)²] }×[(a-1)/4]
={ (4-a)/[a(a-2)²] }×[(a-1)/4]
=(4-a)(a-1)/[4a(a-2)²]
当a=2-√3时
原式=[4-(2-√3)](2-√3-1)/[4(2-√3)(2-√3-2)²]
=(2+√3)(1-√3)/[4(2-√3)×3]
=(2-2√3+√3-3)/[12(2-√3)]
=-(1+√3)/[12(2-√3)]
=-(1+√3)(2+√3)/[12(2+√3)(2-√3)]
=-(2+√3+2√3+3)/[12(2²-√3²)]
=-(5+3√3)/[12(4-3)]
=-(5+3√3)/12