(2x²-9x-5)/(6x²+7x+2);⇒
2x²-9x-5=0
x₁,₂=(9⁺₋√81+4·2·5)/4=(9⁺₋11)/4;
x₁=5;x₂=-0.5;⇒
2x²-9x-5=2(x-5)(x+0.5);
6x²+7x+2=0;
x₁,₂=(-7⁺₋√49-4·6·2)/12=(-7⁺₋1)/12;
x₁=-0.5;x₂=-2/3;⇒
6x²+7x+2=6(x+0.5)(x+2/3);⇒
(2x²-9x-5)/(6x²+7x+2)=2(x-5)(x+0.5)/6(x+0.5)(x+2/3)=(x-5)/3(x+2/3)=
=(x-5)/(3x+2)