Question

计算：1.【a- a+1分之a】÷ a²-4分之a³-2a² 2.a²-b

Answer 1

[a-a/(a+1)]÷[(a^3-2a^2)/(a^2-4)]

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

=[(a^2+a-a)/(a+1)]÷a^2/(a+2)

=a^2/(a+1)÷a^2/(a+2)

=a^2/(a+1)*(a+2)/a^2

=(a+2)/(a+1)

1/(a^2-b^2)÷[1/(a+b)+1/(a-b)]

=1/(a^2-b^2)÷[(a-b)/(a-b)(a+b)+(a+b)/(a-b)(a+b)]

=1/(a^2-b^2)÷[(a-b)/(a^2-b^2)+(a+b)/(a^2-b^2)]

=1/(a^2-b^2)÷[(a-b+a+b)/(a^2-b^2)]

=1/(a^2-b^2)÷[2a/(a^2-b^2)]

=1/(a^2-b^2)*(a^2-b^2)/(2a)

=1/(2a)