1.6-bo'lim : Ratsional ifodalar
4. Quyidagi ifodada ko'rsatilgan amalni bajaring va javobni eng kichik shartlarga qisqartiring.
\[\frac{{{x^2} + 5x - 24}}{{{x^2} + 6x + 8}}\,\centerdot \,\frac{{{x^2} + 4x + 4}}{{{x^2} - 3x}}\]Yechim
Shunday qilib, biz birinchi navbatda har bir ko'phadni iloji boricha ko'proq faktorlarga ajratishimiz kerak.
\[\frac{{\left( {x + 8} \right)\left( {x - 3} \right)}}{{\left( {x + 4} \right)\left( {x + 2} \right)}}\,\centerdot \,\frac{{{{\left( {x + 2} \right)}^2}}}{{x\left( {x - 3} \right)}} = \frac{{\left( {x + 8} \right)}}{{\left( {x + 4} \right)}}\,\centerdot \,\frac{{\left( {x + 2} \right)}}{x}\]2-qadam
Nihoyat, ikkita shartni birga ko'paytiring. Shunday qilib,
\[\frac{{{x^2} + 5x - 24}}{{{x^2} + 6x + 8}}\,\centerdot \,\frac{{{x^2} + 4x + 4}}{{{x^2} - 3x}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{\left( {x + 8} \right)\left( {x + 2} \right)}}{{x\left( {x + 4} \right)}}}}\]