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Приведи данные дроби к знаменателю \(x^{2}y+xy^{2}\) :

1. \(\cfrac{1}{xy}\) ;

2. \(\cfrac{y}{x^{2}+xy}\) ;

3. \(\cfrac{x-y}{xy}\) ;

4. \(\cfrac{x+y}{y}\) .

Решение.

Имеем \(x^{2}y + xy^{2} = xy(x + y)\) .

1. \(\cfrac{1^{\setminus}}{xy} = \cfrac{\ldots}{xy(x+y)} = \cfrac{\ldots}{x^{2}y+xy^{2}}\) .

2. \(\cfrac{y}{x^{2}+xy} = \cfrac{y^{\setminus}}{x(x+y)} = \cfrac{\ldots}{xy(x+y)} = \cfrac{\ldots}{x^{2}y+xy^{2}}\) .

Ответ:

1. \(\cfrac{1}{xy}\) \(=\) [ ];

2. \(\cfrac{y}{x^{2}+xy}\) \(=\) [ ];

3. \(\cfrac{x-y}{xy}\) \(=\) [ ];

4. \(\cfrac{x+y}{y}\) \(=\) [ ].