If a + b + c = 3 and none of a, b and c is equal to 1, then what is the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)}} + \frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)}} + \frac{1}{{\left( {1 - c} \right)\left( {1 - a} \right)}}?$$
A. 0
B. 1
C. 3
D. 6
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & a + b + c = 3 \cr & {\text{Put }}a = 4,\,b = - 1,\,c = 0 \cr & \frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)}} + \frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)}} + \frac{1}{{\left( {1 - c} \right)\left( {1 - a} \right)}} \cr & = \frac{1}{{ - 3 \times 2}} + \frac{1}{{2 \times 1}} - \frac{1}{3} \cr & = \frac{1}{2} - \frac{1}{3} - \frac{1}{6} \cr & = \frac{0}{6} \cr & = 0 \cr} $$Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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