What is \frac{x^{2}-y^{2}-z^{2}-2yz}{x^{2}+y^{2}-z^{2}+2xy}+\frac{x^{2}-y^{2}-z^{2}-2yz}{x^{2}-y^{2}+z^{2}-2xz} equal to ?
- A. \frac{x}{x+y-z}
- B. \frac{y+z}{x+y-z}
- C. \frac{2x}{x+y-z} ✓
- D. \frac{2y+2z}{x+y-z}
Correct Answer: C. \frac{2x}{x+y-z}
Explanation
The common numerator is x^2-(y+z)^2 = (x-y-z)(x+y+z). The denominators factor as (x+y)^2-z^2 = (x+y-z)(x+y+z) and (x-z)^2-y^2 = (x-y-z)(x+y-z). The sum simplifies to \frac{x-y-z}{x+y-z} + \frac{x+y+z}{x+y-z} = \frac{2x}{x+y-z}.
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