1.6-bo'lim : Ratsional ifodalar
7. Quyidagi ifodada ko'rsatilgan amalni bajaring va javobni eng kichik shartlarga qisqartiring.
\[\frac{{\displaystyle \frac{3}{{x + 1}}}}{{\displaystyle \frac{{x + 4}}{{{x^2} + 11x + 10}}}}\]Yechim
Bu shunchaki bo'linish va shuning uchun avval uni mahsulotga aylantiramiz.
\[\frac{{\displaystyle \frac{3}{{x + 1}}}}{{\displaystyle \frac{{x + 4}}{{{x^2} + 11x + 10}}}} = \frac{3}{{x + 1}}\,\centerdot \,\frac{{{x^2} + 11x + 10}}{{x + 4}}\]2-qadam
Endi biz ikkinchi atamaning har birini imkon qadar ko'proq faktor bilan hisoblashimiz mumkin,
\[\frac{{\displaystyle \frac{3}{{x + 1}}}}{{\displaystyle \frac{{x + 4}}{{{x^2} + 11x + 10}}}} = \frac{3}{{x + 1}}\,\centerdot \,\frac{{\left( {x + 1} \right)\left( {x + 10} \right)}}{{x + 4}}\]3-qadam
Endi eng past shartlarga qisqartirish va mahsulotni bajarish uchun iloji boricha bekor qiling.
\[\frac{{\displaystyle \frac{3}{{x + 1}}}}{{\displaystyle \frac{{x + 4}}{{{x^2} + 11x + 10}}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{3\left( {x + 10} \right)}}{{x + 4}}}}\]