Question

x+1/3x2-4x-7 сократите дробь

Answer 1

(х+1)/(3х²-4х-7) = (х+1)/(х-2 1/3)(х+1)*3 = 1/(х-2 1/3)*3 = 1/(3х-7),

где:

3х²-4х-7 = 0,

Д = (-4)² - 4*3*(-7) = 16 + 84 = 100,

х1 = (4+10)/2*3 = 2 1/3,

х2 = (4 - 10)/2*3 = -6/6 = -1, значит:

3х²-4х-7 = 3*(х-2 1/3)(х+1)

Answer 2

$\frac{x + 1}{3 {x}^{2} + 3x - 7x - 7 } = \\ = \frac{x + 1}{3x(x + 1) - 7(x + 1)} = \\ = \frac{x + 1}{(x + 1)(3x - 7)} = \\ = \frac{1}{3x - 7}$