Question

Скоротить дроб
3x^2+2x-1
––––––––
3-x-4x^2

Answer 1

Ответ:

$-\frac{3x - 1}{4x - 3}.$

Объяснение:

$1)\ 3x^2 + 2x - 1 = 3(x-\frac{1}{3})(x+1). \\3x^2+2x-1 = 0;\\D = 4 + 4 \cdot 3 = 12 + 4 = 16 = 4^2.\\x_1=\frac{-2 + 4}{2 \cdot 3} = \frac{2}{6} = \frac{1}{3};\\\\x_2 = \frac{-2 -4}{2 \cdot 3} = -\frac{6}{6} = -1.\\\\2)\ 3 - x - 4x^2 = -4(x-\frac{3}{4})(x+1)\\-4x^2 - x + 3 = 0;\\D = 1 + 4 \cdot 3 \cdot 4 = 48 + 1 = 49 = 7^2.\\x_1 = \frac{1 + 7}{-4 \cdot 2} = - \frac{8}{8} = -1;\\\\x_2 = \frac{1 - 7}{-4 \cdot 2} = \frac{6}{8} = \frac{3}{4}.$

$3)\ \frac{3x^2+2x-1}{3-x-4x^2} = \frac{3(x-\frac{1}{3})(x+1)}{-4(x-\frac{3}{4})(x+1)} = -\frac{3(x-\frac{1}{3})}{4(x-\frac{3}{4})} = -\frac{3x - 1}{4x - 3}.$