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The question is: Prove

[tex]\frac{1}{x}-\frac{1}{y}[/tex] is directly proportional to [tex]\frac{1}{x}[/tex]

This how I went about it:

[tex]\frac{1}{x}-\frac{1}{y}=\frac{y-x}{xy}[/tex]

[tex]\frac{y-x}{xy}=[\frac{y-x}{y}]\frac{1}{x}[/tex]

Can we say the quantity on the right hand side is proportional to [tex]\frac{1}{x}[/tex]?