1.6-bo'lim : Ratsional ifodalar
12. Quyidagi ifodada ko'rsatilgan amalni bajaring.
\[\frac{{x + 10}}{{{{\left( {3x + 8} \right)}^3}}} + \frac{x}{{{{\left( {3x + 8} \right)}^2}}}\]Yechim
Bu ratsional ifoda uchun birinchi navbatda eng kichik umumiy maxraj kerak.
\[{\mbox{lcd : }}{\left( {3x + 8} \right)^3}\]Esda tutingki, biz eng kichik umumiy maxrajni o'rnatishda faqat maxrajdagi har bir atama uchun eng yuqori quvvatni olamiz.
2-qadam
Endi har bir atamaning maxrajiga eng kichik umumiy maxrajni olish uchun uni tegishli miqdorga ko'paytiring.
\[\frac{{x + 10}}{{{{\left( {3x + 8} \right)}^3}}} + \frac{x}{{{{\left( {3x + 8} \right)}^2}}} = \frac{{x + 10}}{{{{\left( {3x + 8} \right)}^3}}} + \frac{{x\left( {3x + 8} \right)}}{{{{\left( {3x + 8} \right)}^2}\left( {3x + 8} \right)}}\]3-qadam
Endi biz qilishimiz kerak bo'lgan narsa qo'shishni amalga oshirish va natijaning hisobini soddalashtirishdir.
\[\frac{{x + 10}}{{{{\left( {3x + 8} \right)}^3}}} + \frac{x}{{{{\left( {3x + 8} \right)}^2}}} = \frac{{x + 10 + 3{x^2} + 8x}}{{{{\left( {3x + 8} \right)}^3}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{3{x^2} + 9x + 10}}{{{{\left( {3x + 8} \right)}^3}}}}}\]