SOLUTION: Simplify: (a^-2-b^-2)/(a^-1+b^-1)

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Question 479530: Simplify: (a^-2-b^-2)/(a^-1+b^-1)
Answer by Maths68(1474) About Me  (Show Source):
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Let A=a^-2-b^-2
A=1/(a^2)-1/(b^2)
Taking LCM
A=b^2-a^2 / a^2b^2
A=[(b-a) (b+a)]/a^2b^2
A=[(b-a) (b+a)]/[(ab)(ab)]
Let B=(a^-1+b^-1)
B= (1/a+1/b)
Taking LCM
B = b+a/ab
1/B=ab/(a+b)
=A/B
=(A) * (1/B)
= [(b-a) (b+a)]/[(ab)(ab)]
=[ab(b-a)(a+b)]/[(ab)(ab)(a+b)]
=(b-a)/ab