1.6-bo'lim : Ratsional ifodalar
8. Quyidagi ifodada ko'rsatilgan amalni bajaring.
\[\frac{3}{{x - 4}} + \frac{x}{{2x + 7}}\]Yechim
Bu ratsional ifoda uchun birinchi navbatda eng kichik umumiy maxraj kerak.
\[{\mbox{lcd : }}\left( {x - 4} \right)\left( {2x + 7} \right)\]2-qadam
Endi har bir atamaning maxrajiga eng kichik umumiy maxrajni olish uchun uni tegishli miqdorga ko'paytiring.
\[\frac{3}{{x - 4}} + \frac{x}{{2x + 7}} = \frac{{3\left( {2x + 7} \right)}}{{\left( {x - 4} \right)\left( {2x + 7} \right)}} + \frac{{x\left( {x - 4} \right)}}{{\left( {2x + 7} \right)\left( {x - 4} \right)}}\]3-qadam
Endi biz qilishimiz kerak bo'lgan narsa qo'shishni amalga oshirish va natijaning hisobini soddalashtirishdir.
\[\frac{3}{{x - 4}} + \frac{x}{{2x + 7}} = \frac{{3\left( {2x + 7} \right) + x\left( {x - 4} \right)}}{{\left( {x - 4} \right)\left( {2x + 7} \right)}} = \frac{{6x + 21 + {x^2} - 4x}}{{\left( {x - 4} \right)\left( {2x + 7} \right)}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{{x^2} + 2x + 21}}{{\left( {x - 4} \right)\left( {2x + 7} \right)}}}}\]