Question

先化简后,再求值:(a-2/a*a+2a-a-1/a*a+4a+4)/a-4/a+2其中a=根号2-1

Answer 1

化简

[(a-2)/(a*a+2a)-(a-1)/(a*a+4a+4)]/[(a-4)/(a+2)]

={(a-2)/[a(a+2)]-(a-1)/(a+2)²} ×[(a+2)/(a-4)]

=[(a²-4)-a(a-1)]/[a(a+2)²] ×[(a+2)/(a-4)]

=(a-4)/[a(a+2)²]×(a+2)/(a-4)

=1/[(a(a+2)

∵a=√2-1

∴a+2=√a+1

∴a(a+2)=(√2-1)(√2+1)=1

∴原式=1/[(a(a+2)]=1