Question

упростить:2х^2+х-3 / 6х^2+13х +6

Answer 1

ax²+bx+c =a(x -x₁)(x -x₂)
2х²+х-3=0
D=1²-4*2*(-3)=1+24=25      

$x_{1} = \frac{-1-5}{2*2} = \frac{-6}{4} =- \frac{3}{2}$

$x_{2}= \frac{-1+5}{2*2} = \frac{4}{4} =1$

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

6x²+13x+6=0
D=13²-4*6*6=169-144=25

$x_{1} = \frac{-13-5}{2*6} = \frac{-18}{12} =- \frac{3}{2}$

$x_{2} = \frac{-13+5}{2*6} = \frac{-8}{12} =- \frac{2}{3}$

$6x^2+13x+6=6(x+ \frac{3}{2} )(x+ \frac{2}{3} )=(2x+3)(3x+2)$

$\frac{2 x^{2} +x-3}{6x^2+13x+6} = \frac{(2x+3)(x-1)}{(2x+3)(3x+2)} = \frac{x-1}{3x+2}$