Question

已知3a=4b,a+b分之a+a-b分之b+a的平方-b的平方分之a的平方

Answer 1

解：
3a=4b
a/b=4/3
原式=a/(a+b)+b/(a-b)+a²/(a²-b²)
=a(a-b)/[(a+b)(a-b)]+b(a+b)/[(a+b)(a-b)]+a²/[(a+b)(a-b)]
=[a(a-b)+b(a+b)+a²]/[(a+b)(a-b)]
=(a²-ab+ab+b²+a²)/[(a+b)(a-b)]
=(2a²+b²)/(a²-b²)
=[(2a²+b²)×1/b²]/[(a²-b²)×1/b²]
=[2×(a²/b²)+1]/[(a²/b²)-1]
=[2×(4/3)²+1]/[(4/3)²-1]
=(41/9)/(7/9)
=41/7

Answer 2

3a=4b
,a+b分之a+a-b分之b+a的平方-b的平方分之a的平方
=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^2-ab+ab+b^2+a^2)/(a+b)(a-b)
=(2a^2+b^2)/(a+b)(a-b),3a=4b,a=4b/3
=(41b^2/9)/(7b^2/9)
=41/7

Answer 3

解：∵3a=4b, ∴b=3a/4
a/(a+b)+b/(a-b)+a^2/(a^2-b^2)
=( a^2+b^2)/(a^2-b^2) +a^2/(a^2-b^2)
= (2a^2+b^2)/( a^2-b^2)…将b=3a/4
=(2a^2+9a^2/16)/( a^2-9a^2/16)
=41/7