Бөлшекті жазайық:

\(\displaystyle \begin{array}{l}\frac{x^{\,9}y^{\,9}z^{\,11}-\frac{5}{6}x^{\,8}y^{\,8}z^{\,9}-\frac{3}{4}x^{\,7}y^{\,6}z^{\,5}-\frac{9}{11}x^{\,4}y^{\,5}z^{\,5}}{\frac{5}{7}x^{\,3}y^{\,3}z^{\,2}}=\\\kern{10em} =\frac{x^{\,9}y^{\,9}z^{\,11}}{\phantom{1}\frac{5}{7}x^{\,3}y^{\,3}z^{\,2}\phantom{1}}-\frac{\frac{5}{6}x^{\,8}y^{\,8}z^{\,9}}{\phantom{1}\frac{5}{7}x^{\,3}y^{\,3}z^{\,2}\phantom{1}}-\frac{\frac{3}{4}x^{\,7}y^{\,6}z^{\,5}}{\phantom{1}\frac{5}{7}x^{\,3}y^{\,3}z^{\,2}\phantom{1}}-\frac{\frac{9}{11}x^{\,4}y^{\,5}z^{\,5}}{\phantom{1}\frac{5}{7}x^{\,3}y^{\,3}z^{\,2}\phantom{1}}{\small .}\end{array}\)

Әр мүшеде бөлшек түрінде сандық коэффициенттерді шығарайық:

\(\displaystyle \begin{array}{l}\frac{x^{\,9}y^{\,9}z^{\,11}}{\phantom{1}\frac{5}{7}x^{\,3}y^{\,3}z^{\,2}\phantom{1}}-\frac{\frac{5}{6}x^{\,8}y^{\,8}z^{\,9}}{\phantom{1}\frac{5}{7}x^{\,3}y^{\,3}z^{\,2}\phantom{1}}-\frac{\frac{3}{4}x^{\,7}y^{\,6}z^{\,5}}{\phantom{1}\frac{5}{7}x^{\,3}y^{\,3}z^{\,2}\phantom{1}}-\frac{\frac{9}{11}x^{\,4}y^{\,5}z^{\,5}}{\phantom{1}\frac{5}{7}x^{\,3}y^{\,3}z^{\,2}\phantom{1}}=\\\kern{10em} = \frac{1}{\phantom{1}\frac{5}{7}\phantom{1}}\frac{x^{\,9}y^{\,9}z^{\,11}}{x^{\,3}y^{\,3}z^{\,2}}- \frac{\frac{5}{6}}{\phantom{1}\frac{5}{7}\phantom{1}}\frac{x^{\,8}y^{\,8}z^{\,9}}{x^{\,3}y^{\,3}z^{\,2}}-\frac{\frac{3}{4}}{\phantom{1}\frac{5}{7}\phantom{1}}\frac{x^{\,7}y^{\,6}z^{\,5}}{x^{\,3}y^{\,3}z^{\,2}}-\frac{\frac{9}{11}}{\phantom{1}\frac{5}{7}\phantom{1}}\frac{x^{\,4}y^{\,5}z^{\,5}}{x^{\,3}y^{\,3}z^{\,2}}{\small .}\end{array}\)

Сандық коэффициенттерді бір-біріне бөлейік және дәрежелерге дәрежелер бөліндісі формуласын қолданамыз:

\(\displaystyle \begin{array}{l}\frac{1}{\phantom{1}\frac{5}{7}\phantom{1}}\frac{x^{\,9}y^{\,9}z^{\,11}}{x^{\,3}y^{\,3}z^{\,2}}- \frac{\frac{5}{6}}{\phantom{1}\frac{5}{7}\phantom{1}}\frac{x^{\,8}y^{\,8}z^{\,9}}{x^{\,3}y^{\,3}z^{\,2}}-\frac{\frac{3}{4}}{\phantom{1}\frac{5}{7}\phantom{1}}\frac{x^{\,7}y^{\,6}z^{\,5}}{x^{\,3}y^{\,3}z^{\,2}}-\frac{\frac{9}{11}}{\phantom{1}\frac{5}{7}\phantom{1}}\frac{x^{\,4}y^{\,5}z^{\,5}}{x^{\,3}y^{\,3}z^{\,2}}=\\[10px]\kern{4em} =\left(1:\frac{5}{7}\right)x^{\,9-3}y^{\,9-3}z^{\,11-2}-\left(\frac{5}{6}:\frac{5}{7}\right)x^{\,8-3}y^{\,8-3}z^{\,9-2}-\\[10px]\kern{13em} -\left(\frac{3}{4}:\frac{5}{7}\right)x^{\,7-3}y^{\,6-3}z^{\,5-2}-\left(\frac{9}{11}:\frac{5}{7}\right)x^{\,4-3}y^{\,5-3}z^{\,5-2}=\\[10px]\kern{16em} =\frac{7}{5}x^{\,6}y^{\,6}z^{\,9}-\frac{7}{6}x^{\,5}y^{\,5}z^{\,7}-\frac{21}{20}x^{\,4}y^{\,3}z^{\,3}-\frac{63}{55}xy^{\,2}z^{\,3}{\small .}\end{array}\)

Жауабы: \(\displaystyle \frac{7}{5}x^{\,6}y^{\,6}z^{\,9}-\frac{7}{6}x^{\,5}y^{\,5}z^{\,7}-\frac{21}{20}x^{\,4}y^{\,3}z^{\,3}-\frac{63}{55}xy^{\,2}z^{\,3}{\small .}\)