1.6-bo'lim : Ratsional ifodalar
6. Quyidagi ifodada ko'rsatilgan amalni bajaring va javobni eng kichik shartlarga qisqartiring.
\[\frac{{{x^2} - 2x - 8}}{{2{x^2} - 8x - 24}} \div \frac{{{x^2} - 9x + 20}}{{{x^2} - 11x + 30}}\]Yechim
Shunday qilib, biz birinchi navbatda buni mahsulotga aylantirishimiz kerak.
\[\frac{{{x^2} - 2x - 8}}{{2{x^2} - 8x - 24}} \div \frac{{{x^2} - 9x + 20}}{{{x^2} - 11x + 30}} = \frac{{{x^2} - 2x - 8}}{{2{x^2} - 8x - 24}}\,\centerdot \,\frac{{{x^2} - 11x + 30}}{{{x^2} - 9x + 20}}\]Bo'linishni mahsulotga aylantirmaguningizcha ko'paytuvchilarga ajratish va bekor qilmasligingizga ishonch hosil qiling.
2-qadam
Endi biz shartlarning har birini olish uchun iloji boricha ko'proq faktor bo'lishimiz mumkin,
\[\frac{{{x^2} - 2x - 8}}{{2{x^2} - 8x - 24}} \div \frac{{{x^2} - 9x + 20}}{{{x^2} - 11x + 30}} = \frac{{\left( {x - 4} \right)\left( {x + 2} \right)}}{{2\left( {x + 2} \right)\left( {x - 6} \right)}}\,\centerdot \,\frac{{\left( {x - 5} \right)\left( {x - 6} \right)}}{{\left( {x - 5} \right)\left( {x - 4} \right)}}\]3-qadam
Nihoyat, eng past shartlarga qisqartirish va mahsulotni bajarish uchun iloji boricha bekor qiling.
\[\frac{{{x^2} - 2x - 8}}{{2{x^2} - 8x - 24}} \div \frac{{{x^2} - 9x + 20}}{{{x^2} - 11x + 30}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{1}{2}}}\]Agar siz eng past shartlarga qisqartirganingizdan so'ng, barcha o'zgaruvchilar bekor qilinsa, tashvishlanmang. Bu vaqti-vaqti bilan sodir bo'ladi, shuning uchun bu sodir bo'lganda tashvishlanmang.