Question

计算分式：b^4/(a-b)^2 乘 a^3+ab^2-2a^2b/b^3 除以b^2-a^2/ab+b^2

Answer 1

^4/(a-b)^2乘(a^3+ab^2-2a^2b)/b^3除以(b^2-a^2)/(ab+b^2)

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

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

=(ab^4/b^3)除以(b^2-a^2)/(ab+b^2)

=ab除以(b^2-a^2)/(ab+b^2)

=ab乘(ab+b^2)/(b^2-a^2)

=ab乘[b(a+b)]/[(b-a)(b+a)]

=ab乘[b/(b-a)]

=ab^2/(b-a)