Question

(2/3a)-[2/(a+b)]{[(a+b)/3a]-a-b}÷[(a-b)/b]

Answer 1

原式=2/3a-[2/(a+b)]{[(a+b)/3a]-(a+b)}÷[(a-b)/b]
乘进去
=2/3a-[2/3a-2]×[b/(a-b)]
=2/3a-(2-6a)/3a×[b/(a-b)]
=2/3a-(2b-6ab)/3a(a-b)
=(2a-2b-2b+6ab)/(3a^2-3ab)
=(2a-4b+6ab)/(3a^2-3ab)

Answer 2

[2/3a - 2/(a+b) * (a+b/3a - a - b)] / (a-b)/a
=[2/3a-2/(a+b)*(a+b)*(1/3a-1)]/(a-b)/a
=a[2/3a-2(1/3a-1)]/(a-b)
=a*2/(a-b)
=2a/(a-b)