Question

怎样化简：a/[b(a-b)]-b/[a(a-b)]

Answer 1

a/[b(a-b)]-b/[a(a-b)]
化同分母，原式=a²/[ab(a-b)]-b²/[ab(a-b)]
=(a²-b²)/[ab(a-b)]
=(a+b)(a-b)/[ab(a-b)] =(a+b)/ab

Answer 2

a/[b(a-b)]-b/[a(a-b)]
=(a/b-b/a)/(a-b)
=（a²-b²）/ab（a-b）
=（a+b）/ab

Answer 3

a/[b(a-b)]-b/[a(a-b)]=a²/[ab(a-b)]-b²/[ab(a-b)]=(a²-b²)/[ab(a-b)]=(a+b)/(ab)

Answer 4

提取公因式 （a-b)
a/[b(a-b)]-b/[a(a-b)]

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