What is expand (1/x-1/y)/(1-x/y) ?

The solution to expand (1/x-1/y)/(1-x/y) is 1/x

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expand (1/x-1/y)/(1-x/y)

expand

\frac{\frac{1}{x} - \frac{1}{y}}{1 - \frac{x}{y}}

\frac{1}{x}

Solution steps

\frac{\frac{1}{x} - \frac{1}{y}}{1 - \frac{x}{y}}

Join

1 - \frac{x}{y} : \frac{y - x}{y}

= \frac{\frac{1}{x} - \frac{1}{y}}{\frac{y - x}{y}}

Join

\frac{1}{x} - \frac{1}{y} : \frac{y - x}{x y}

= \frac{\frac{y - x}{x y}}{\frac{y - x}{y}}

Divide fractions:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( y - x ) y}{x y ( y - x )}

Cancel the common factor:

y - x

= \frac{y}{x y}

Cancel the common factor:

y

= \frac{1}{x}

\frac{6 ( x ^{2} + y ^{2} )}{2 x - 3 y}

\frac{x ( x - 1 )}{( x + 5 ) ( x - 4 )}

(x - 3 - i) (x - 3 + i)

(cos (x) cos (y) - cot (x)) d x - sin (x) sin (y) d y

What is expand (1/x-1/y)/(1-x/y) ?
The solution to expand (1/x-1/y)/(1-x/y) is 1/x