Question

化简[(a-b)/(a+2b)]/[(a^2-b^2)/(a^2+4ab+b^2)]-(3a^2-4ab)/(a^2+a

Answer 1

[(a-b)/(a+2b)]/[(a^2-b^2)/(a^2+4ab+4b^2)]-(3a^2-4ab)/(a^2+ab)

=[(a-b)/(a+2b)]×[(a+2b)²/(a-b)(a+b)]-(3a²-4ab)/(a²+ab)

=(a+2b)/(a+b)-a(3a-4b)/a(a+b)

=(a+2b)/(a+b)-(3a-4b)/(a+b)

=(a+2b-3a+4b)/(a+b)

=(-2a+6b)/(a+b)