LM wrote:
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
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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