Problem: If 1x−1y=1z\dfrac{1}{x}-\dfrac{1}{y}=\dfrac{1}{z}x1−y1=z1, then zzz equals:
Answer Choices:
A. y−xy-xy−x
B. x−yx-yx−y
C. y−xxy\dfrac{y-x}{x y}xyy−x
D. xyy−x\dfrac{x y}{y-x}y−xxy
E. xyx−y\dfrac{x y}{x-y}x−yxy Solution:
y−xxy=1z; z=xyy−x\dfrac{y-x}{x y}=\dfrac{1}{z} ;~ z=\dfrac{x y}{y-x} xyy−x=z1; z=y−xxy