Question

已知3a=4b,求a/(a+b)+b/(a-b)-a^2/(a^2-b^2)的值

Answer 1

设a=4k,那么b=3k

a/(a+b)+b/(a-b)-a^2/(a^2-b^2)

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

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

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

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

=9k²/7k²

=9/7