Question

if 1/a 1/b 1/c are in ap, then find the value of a - b/b - c

Answer 1

Answer:

Consider 1/a+b,1/b+c,1/c+a are in AP

So we know that in AP 2nd term-1st term

So we have  

By taking LCM for the denominators of the above expression and simplifying

We get a+b – (b+c)/(b+c)(a+b)=b+c-(c+a)/(c+a)(b+c)

By cancellation of the known terms

By cross multiplication

=(a-c)(c+a)=(a+b)(b-a)

 [by multiplication of the terms]

By cancelling the terms we get