Question

Сократить дробь: \frac{6+7x+2x^2}{2x+3}

Answer 1

$\frac{2 {x}^{2} + 7x + 6 }{2x + 3} = \frac{(x + 2)(2x + 3)}{2x + 3} = x + 2. \\ \\ 2 {x}^{2} + 7x + 6 = 0 \\ d = 49 - 48 = 1 \\ x1 = \frac{ - 7 + 1}{4} = - \frac{3}{2} \\ x2 = \frac{ - 7 - 1}{4} = \frac{ - 8}{4} = -2 \\ 2(x +2)(x + \frac{3}{2} ) = (x + 2)(2x + 3)$