SOLUTION: If b is the harmonic mean between a and c,then prove that:1/(b-a) +1/(b-c)=1/a+1/c

Question 1083841: If b is the harmonic mean between a and c,then prove that:1/(b-a) +1/(b-c)=1/a+1/c
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

We find the arithmetic mean of  and 

Add them 

Divide by 2:  

Its reciprocal  is the harmonic mean
between a and c, so



Substitute for b in





Multiply numerators and denominators by (a+c)















Factor out 

















Edwin

RELATED QUESTIONS
If a,b,c are in Harmonic Progression,prove that 1/a + 1/(b+c), 1/b + 1(c+a), 1/c + 1(a+b) (answered by mccravyedwin)

If a,b,c, are in harmonic progression shown that (1/a+1/b-1/c)(1/b+1/c... (answered by Edwin McCravy)

If a,b,c are in Harmonic Progression, show that 1/a + 1/(b+c) , 1/b + 1/(c+a) , 1/c +... (answered by CPhill)

If a,b,c parallel line. then prove that a(1/b + 1/c), b(1/c + 1/a), c(1/a + 1/b) in... (answered by ikleyn)

Prove: If a*c = b*c and c ? 0, then a = b 1| a*c = b*c 2| a*c*(1/c) =... (answered by jim_thompson5910)

prove that abc / a^-1*b^-1 + b^-1*c^-1+ c^-1*a^-1... (answered by ikleyn)

If b+c-a/a, c+a-b/b, a+b-c/c are in A.P. Prove that 1/a,1/b,1/c are also in... (answered by mananth)

If a^2,b^2,c^2 are in AP then prove that 1/b+c,1/c+a,1/a+b are also in... (answered by Edwin McCravy)

Multiple Choice: Match the reason with the proof given below. Prove: If a*c = b*c and c... (answered by solver91311)