Question

(a-2/a^2+2a-a-1/a^2-4a+4)÷a-4/a+2,其中a=√2-1 （求过程）

Answer 1

(a-2/a^2+2a-a-1/a^2+4a+4)÷a-4/a+2

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

=[(a-2)/a-(a-1)/(a+2)] ×1/(a-4)

=(a^2-4-a^2+a)/a(a+2) ×1/(a-4)

=(a-4)/a(a+2) ×1/(a-4)

=1/a(a+2)

=1/(√2-1)(√2+1)

=1/(2-1)

=1