1-тәсіл.

Бөлуді бөлшек сызығына ауыстырайық:

\(\displaystyle \frac{7}{11}x^{\,7}y^{\,8}z^{\,9} : \left(\frac{8}{15}x^{\,3}y^{\,4}z^{\,5}\right)=\frac{\phantom{123}\frac{7}{11}x^{\,7}y^{\,8}z^{\,9}\phantom{123}}{\frac{8}{15}x^{\,3}y^{\,4}z^{\,5}} {\small .}\)

Сандық коэффициенттерді бір бөлшекке, ал айнымалыларды екіншісіне топтастырамыз:

\(\displaystyle \frac{\phantom{123}\color{blue}{\frac{7}{11}}\color{green}{x^{\,7}y^{\,8}z^{\,9}}\phantom{123}}{\color{blue}{\frac{8}{15}}\color{green}{x^{\,3}y^{\,4}z^{\,5}}}=\frac{\phantom{123}\color{blue}{\frac{7}{11}}\phantom{123}}{\color{blue}{\frac{8}{15}}} \frac{\color{green}{x^{\,7}y^{\,8}z^{\,9}}}{\color{green}{x^{\,3}y^{\,4}z^{\,5}}}{\small .}\)

Сандық бөлшектің мәнін табайық

\(\displaystyle \frac{\phantom{123}\color{blue}{\frac{7}{11}}\phantom{123}}{\color{blue}{\frac{8}{15}}}=\color{blue}{\frac{7}{11}}:\color{blue}{\frac{8}{15}}=\color{blue}{\frac{7}{11}}\cdot\color{blue}{\frac{15}{8}}=\frac{\color{blue}{105}}{\color{blue}{88}}\)

және дәрежелер бөліндісінің формуласын қолданамыз:

\(\displaystyle \frac{\color{green}{x^{\,7}y^{\,8}z^{\,9}}}{\color{green}{x^{\,3}y^{\,4}z^{\,5}}}=\color{green}{x^{\,7-3}y^{\,8-4}z^{\,9-5}}=\color{green}{x^{\,4}y^{\, 4}z^{\,4}}{\small .}\)

Алынған нәтижелерді алмастырайық:

\(\displaystyle \frac{\phantom{123}\color{blue}{\frac{7}{11}}\phantom{123}}{\color{blue}{\frac{8}{15}}} \frac{\color{green}{x^{\,7}y^{\,8}z^{\,9}}}{\color{green}{x^{\,3}y^{\,4}z^{\,5}}}=\color{blue}{\frac{105}{88}}\color{green}{x^{\,4}y^{\, 4}z^{\,4}}{\small .}\)

Осылайша,

\(\displaystyle \frac{7}{11}x^{\,7}y^{\,8}z^{\,9}: \left(\frac{8}{15}x^{\,3}y^{\,4}z^{\,5}\right)=\frac{105}{88}x^{\,4}y^{\, 4}z^{\,4}{\small .}\)

2-тәсіл.

 \(\displaystyle \color{green}{\frac{8}{15}} \cdot \color{blue}{x^{\,3}y^{\,4}z^{\,5}}{\small }\) көбейтіндісіне бөлу үшін  көбейткіштердің әрқайсысына бөлу керек:

\(\displaystyle \frac{7}{11}x^{\,7}y^{\,8}z^{\,9} : \left(\color{green}{\frac{8}{15}}\color{blue}{x^{\,3}y^{\,4}z^{\,5}}\right)=\left( \frac{7}{11}x^{\,7}y^{\,8}z^{\,9} : \color{green}{\frac{8}{15}} \right) :\left(\color{blue}{x^{\,3}y^{\,4}z^{\,5}}\right){\small .}\)

1. Алдымен \(\displaystyle \frac{8}{15} {\small }\) бөлеміз  

\(\displaystyle \frac{7}{11}x^{\,7}y^{\,8}z^{\,9} : \color{green}{\frac{8}{15}} =\left(\frac{7}{11}: \color{green}{\frac{8}{15}}\right)x^{\,7}y^{\,8}z^{\,9}=\left(\frac{7}{11}\cdot \color{green}{\frac{15}{8}}\right)x^{\,7}y^{\,8}z^{\,9}=\frac{105}{88}x^{\,7}y^{\,8}z^{\,9}{\small .}\)

2. Алынған нәтижені \(\displaystyle x^{\,3}y^{\,4}z^{\,5}{\small }\) бөлеміз

\(\displaystyle \frac{105}{88}x^{\,7}y^{\,8}z^{\,9}:\left(\color{blue}{x^{\,3}y^{\,4}z^{\,5}}\right)=\frac{105}{88}\frac{x^{\,7}y^{\,8}z^{\,9}}{x^{\,3}y^{\,4}z^{\,5}}=\frac{105}{88}x^{\,7-3}y^{\,8-4}z^{\,9-5}=\frac{105}{88}x^{\,4}y^{\, 4}z^{\,4}{\small .}\)

Осылайша,

\(\displaystyle \frac{7}{11}x^{\,7}y^{\,8}z^{\,9} : \left(\frac{8}{15}x^{\,3}y^{\,4}z^{\,5}\right)=\frac{105}{88}x^{\,4}y^{\, 4}z^{\,4}{\small .}\)

Жауабы: \(\displaystyle \frac{105}{88}x^{\,4}y^{\, 4}z^{\,4} {\small .}\)