Question

Сократите дробь

(6х²-5х-6) / (2х²+5х-12)

Answer 1

$6 x^{2} -5x-6=0\\ D = (-5) ^{2} - 4 *6*(-6)=25+144=169=13 ^{2}\\x _{1} = \frac{5+13}{12}= \frac{18}{12} =1,5\\x _{2}= \frac{5-13}{12}=- \frac{2}{3} \\\\2 x^{2} +5x-2=0\\D=5 ^{2} -4*2*(-12)= 25+96 = 121=11 ^{2}\\x _{1} = \frac{-5+11}{4}=1,5\\x _{2}= \frac{-5-11}{4} =-4\\\\ \frac{6 x^{2} -5x-6}{2 x^{2} +5x-2} = \frac{6(x-1,5)(x+ \frac{2}{3}) }{2(x-1,5)(x+4)}= \frac{3x+2}{x+4}$