[latex] \frac{-12 p^{2} + 40p-25 }{20+7p-6 p^{2} } [/latex] Cократите дробь

раскладываем числитель и знаменатель на множители [latex]-12p^2 + 40p - 25 = 0 \\ 12p^2 - 40p + 25 = 0\\ p_1 = \frac{5}{6}; p_2 = \frac{15}{6} \\ -6p^2 + 7p + 20 = 0 \\ 6p^2 - 7p - 20 = 0 \\ p_1 = \frac{15}{6} ; p_2 = \frac{-4}{3} \\ \frac{-12(p-\frac{5}{6})(p - \frac{15}{6})}{-6(p -\frac{15}{6})(p + \frac{4}{3})} \\ \frac{2(p-\frac{5}{6})}{(p + \frac{4}{3})} \\ \frac{2\frac{6p-5}{6}}{\frac{3p+4}{3}} \\ \frac{6\frac{6p-5}{6}}{3p+4} \\ \frac{6p-5}{3p+4}[/latex]

[latex] \frac{-12 p^{2} + 40p-25 }{20+7p-6 p^{2} } = \frac{(5-6p)(2p-5)}{(-3p-4)(2p-5)} = \frac{5-6p}{-(3p+4)} [/latex] [latex]\frac{5-6p}{-(3p+4)} *(-1)=\frac{-(5+6p)}{-(-(3p+4))}= \frac{6p-5}{3p+4} [/latex]