This question was previously asked in

Territorial Army Paper I : Official Practice Test Paper - 2

Option 3 : 1

**Concept used**

a^{2} - b^{2} = (a - b) (a + b)

**Calculation**

\(\dfrac{x^2-(y-z)^2}{(x+z)^2-y^2}+\dfrac{y^2-(x-z)^2}{(x+y)^2-z^2}+\dfrac{z^2-(x-y)^2}{(y+z)^2-x^2}\)

\(\frac{{\left( {x - y + z} \right)\left( {x + y - z} \right)}}{{\left( {x + y + z} \right)\left( {x + z - y} \right)}} + \frac{{\left( {y + x - z} \right)\left( {y - x + z} \right)}}{{\left( {x + y + z} \right)\left( {x + y - z} \right)}} + \frac{{\left( {z - x + y} \right)\left( {z + x - y} \right)}}{{\left( {y + z - x} \right)\left( {y + z + x} \right)}}\)

\(\frac{{x + y - z + y - x + z + z + x - y}}{{x + y + z}}\)

∴ Ans = 1