What is the value of a^3+b^3-c^3+3abc/a^2+b^2+c^2+ac+bc-ab

Question

What is the value of  \frac{a^3+b^3-c^3+3abc}{a^2+b^2+c^2+ac+bc-ab} ?

A. a+b-c
B. a-b+c
C. -a+b+c
D. a-b-c
E. -a+b-c

PareshGmat · Accepted Answer

\frac{a^3+b^3-c^3+3abc}{a^2+b^2+c^2+ac+bc-ab}

This also means that  a^2+b^2+c^2+ac+bc-ab  when multiplied with any one of the 5 options, gives answer  a^3+b^3-c^3+3abc

Just focus on  a^2, b^2, c^2  in the LHS &  a^3+b^3-c^3  on RHS

a^2  has to be multiplied by "a" to give  a^3

Similarly, b^{2} * b = b^3

c^{2} * -c = -c^3

Answer = a+b-c

Answer = A

Bunuel · Answer

Plug-in method would be the most efficient way to deal with this problem.

Let  a=2 ,  b=1  and  c=0 . Then  \frac{a^3+b^3-c^3+3abc}{a^2+b^2+c^2+ac+bc-ab}=3 . Now let's see which answer choice yields 3:

A. a+b-c=3 --> correct;
B. a-b+c=1 --> discard;
C. -a+b+c=-1 --> discard;
D. a-b-c=1 --> discard;
E. -a+b-c=-1 --> discard.

Answer: A.

P.S. For plug-in method it might happen that for some particular numbers more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

Hope it helps.

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What is the value of a^3+b^3-c^3+3abc/a^2+b^2+c^2+ac+bc-ab

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What is the value of a^3+b^3-c^3+3abc/a^2+b^2+c^2+ac+bc-ab

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