The value of (x²-(y-z)²)/((x+z)²-y²)+(y²-(x-z)²)/((x+y)²-z²)+(z²-(x-y)²)/((y+z)²-x²) is · ABC26GN1226
Subject: General Aptitude · Chapter: Simplification · Exam: M.B.A. 2006
The value of $\frac{x^{2}-(y-z)^{2}}{(x+z)^{2}-y^{2}}+\frac{y^{2}-(x-z)^{2}}{(x+y)^{2}-z^{2}}+\frac{z^{2}-(x-y)^{2}}{(y+z)^{2}-x^{2}}$ is
(a)- 1
(b)0
(c)1
(d)None of these
Answer
Explanation
Given expression $=\frac{(x+y-z)(x-y+z)}{(x+z+y)(x+z-y)}$ $$\begin{aligned} & +\frac{(y+x-z)(y-x+z)}{(x+y+z)(x+y-z)}+\frac{(z+x-y)(z-x+y)}{(y+z+x)(y+z-x)} \\ & \quad=\frac{(x+y-z)}{(x+y+z)}+\frac{(y-x+z)}{(x+y+z)}+\frac{(x-y+z)}{(x+y+z)} \\ & \quad=\frac{(x+y-z)+(y-x+z)+(x-y+z)}{(x+y+z)} \\ & \quad=\frac{x+y+z}{x+y+z}=1 \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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