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# Aptitude - Surds and Indices - Discussion

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"You cannot shake hands with a clenched fist."
- Indira Gandhi
8.

 1 + 1 + 1 = ? 1 + x(b - a) + x(c - a) 1 + x(a - b) + x(c - b) 1 + x(b - c) + x(a - c)

 [A]. 0 [B]. 1 [C]. xa - b - c [D]. None of these

Explanation:

Given Exp. =
1  +  1  +  1
 1 + xb + xc xa xa
 1 + xa + xc xb xb
 1 + xb + xa xc xc

 = xa + xb + xc (xa + xb + xc) (xa + xb + xc) (xa + xb + xc)

 = (xa + xb + xc) (xa + xb + xc)

= 1.

 Raju said: (Sat, Feb 5, 2011 10:00:45 AM) I didn't understand the second line.

 Kunaman said: (Sat, May 7, 2011 10:02:22 AM) @raju We took the lcm of the denominator of the expression 1+x^b/x^a...

 Nisha said: (Tue, Jun 14, 2011 10:29:05 AM) Have any short cut method?

 Vasundhara said: (Sat, Oct 8, 2011 04:26:45 PM) It is the shortcut and easiest way to solve this problem.

 Arshad said: (Fri, May 4, 2012 03:37:14 PM) I did not understood second step from last. Can you please explain in detail(only last two steps) How do you consider x^a+x^b+x^c in numerator ?(x^a+x^b+x^c/x^a+x^b+x^c)

 Sagar said: (Sun, Jun 10, 2012 12:56:30 PM) The second step is derived from first step by multiplying numerator & denominator of each of the 3 components with x^a, x^b & x^c respectively.

 Anagha said: (Sat, May 25, 2013 02:33:27 PM) How do you solve the second step? Really confusing, please do it the long way so we can understand.