រកតម្លៃ x y {\displaystyle {\frac {x}{y}}} បើគេដឹងថា 3 y − 1 x = 2 x + y {\displaystyle {\frac {3}{\sqrt {y}}}-{\frac {1}{\sqrt {x}}}={\frac {2}{{\sqrt {x}}+{\sqrt {y}}}}} ។
( x + y ) ⋅ ( 3 y − 1 x ) = ( 2 x + y ) ⋅ ( x + y ) {\displaystyle ({\sqrt {x}}+{\sqrt {y}})\cdot {\biggl (}{\frac {3}{\sqrt {y}}}-{\frac {1}{\sqrt {x}}}{\biggr )}={\biggl (}{\frac {2}{{\sqrt {x}}+{\sqrt {y}}}}{\biggr )}\cdot ({\sqrt {x}}+{\sqrt {y}})}
3 x + 3 y y − x + y x = 2 ( x + y ) x + y {\displaystyle {\frac {3{\sqrt {x}}+3{\sqrt {y}}}{\sqrt {y}}}-{\frac {{\sqrt {x}}+{\sqrt {y}}}{\sqrt {x}}}={\frac {2({\sqrt {x}}+{\sqrt {y}})}{{\sqrt {x}}+{\sqrt {y}}}}}
3 x y + 3 − 1 − y x = 2 {\displaystyle {\frac {3{\sqrt {x}}}{\sqrt {y}}}+3-1-{\frac {\sqrt {y}}{\sqrt {x}}}=2}
3 x y = y x {\displaystyle {\frac {3{\sqrt {x}}}{\sqrt {y}}}={\frac {\sqrt {y}}{\sqrt {x}}}}
3 x = y {\displaystyle 3x=y}
x y = 1 3 {\displaystyle {\frac {x}{y}}={\frac {1}{3}}}
បើគេដឹងថា 
។
