Question

Срочно!!!!!
Разложение квадратного трёхчлена на множители
3х²+х-2/х²+х

Answer 1

$\displaystyle\bf\\3x^{2} +x-2=0\\\\D=1^{2} -4\cdot 3\cdot (-2)=1+24=25=5^{2} \\\\x_{1} =\frac{-1-5}{6} =-1\\\\x_{2} =\frac{-1+5}{6} =\frac{2}{3}\\\\\boxed{3x^{2} +x-2=3\Big(x+1\Big)\Big(x-\frac{2}{3} \Big)}\\\\\\\frac{3x^{2} +x-2}{x^{2} +x} =\frac{3\Big(x+1\Big)\Big(x-\frac{2}{3} \Big)}{x(x+1)} =\frac{3x-2}{x}$