The value of $$\frac{{{x^2} - {{\left( {y - z} \right)}^2}}}{{{{\left( {x + z} \right)}^2} - {y^2}}}{\text{ + }}$$ $$\frac{{{y^2} - {{\left( {x - z} \right)}^2}}}{{{{\left( {x + y} \right)}^2} - {z^2}}} + $$ $$\frac{{{z^2} - {{\left( {x - y} \right)}^2}}}{{{{\left( {y + z} \right)}^2} - {x^2}}}$$ is = ?
A. -1
B. 0
C. 1
D. None of these
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{Given xepression ,}} \cr & \frac{{\left( {x + y - z} \right)\left( {x - y + z} \right)}}{{\left( {x + y + z} \right)\left( {x + z - y} \right)}} + \frac{{\left( {y + x - z} \right)\left( {y - x + z} \right)}}{{\left( {x + y + z} \right)\left( {x + y - z} \right)}} + \frac{{\left( {z + x - y} \right)\left( {z - x + y} \right)}}{{\left( {y + z + x} \right)\left( {y + z - x} \right)}} \cr & = \frac{{\left( {x + y - z} \right)}}{{\left( {x + y + z} \right)}} + \frac{{\left( {y - x + z} \right)}}{{\left( {x + y + z} \right)}} + \frac{{\left( {x - y + z} \right)}}{{\left( {x + y + z} \right)}} \cr & = \frac{{\left( {x + y - z} \right) + \left( {y - x + z} \right) + \left( {x - y + z} \right)}}{{\left( {x + y + z} \right)}} \cr & = \frac{{x + y + z}}{{x + y + z}} \cr & = 1 \cr} $$Related Questions on Simplification
A. 20
B. 80
C. 100
D. 200
E. None of these
A. Rs. 3500
B. Rs. 3750
C. Rs. 3840
D. Rs. 3900
E. None of these
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