What is the simplified value of $$\frac{{\left( {x + y + z} \right)\left( {xy + yz + zx} \right) - xyz}}{{\left( {x + y} \right)\left( {y + z} \right)\left( {z + x} \right)}}?$$
A. y
B. x
C. 1
D. z
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & \frac{{\left( {x + y + z} \right)\left( {xy + yz + zx} \right) - xyz}}{{\left( {x + y} \right)\left( {y + z} \right)\left( {z + x} \right)}} \cr & {\text{put }}z = 0, \cr & = \frac{{\left( {x + y + 0} \right)\left( {xy + 0 + 0} \right) - 0}}{{\left( {x + y} \right)\left( {y + 0} \right)\left( {0 + x} \right)}} \cr & = \frac{{\left( {x + y} \right)\left( {xy} \right)}}{{\left( {x + y} \right)\left( {xy} \right)}} \cr & = 1 \cr} $$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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