[tex]zad.1\\\\D=R-\{ 0,~~1\frac{1}{2} \}\\\\\dfrac{4x^{2} -9}{2x^{2} -3x} \div \dfrac{15+10x}{3x^{2} } =\dfrac{(2x-3)\cdot (2x+3)}{x(2x-3)} \cdot \dfrac{3x^{2} }{5(3+2x)} =\dfrac{3}{5} x\\\\zad.2\\I.\\f(x)=x^{2} +x-6\\a=1,~~b=1,~~c=-6\\\Delta=1^{2} -4\cdot 1\cdot (-6)=1+24=25,~~\sqrt{\Delta} =5\\\\x_{1} =\dfrac{-1-5}{2} =-3~~\lor~~x_{2} =\dfrac{-1+5}{2} =2\\f(x)=(x+3)\cdot (x-2)\\II.\\f(x)=x^{2} +2x-15\\a=1,~~b=2,~~c=-15\\\Delta=2^{2} -4\cdot 1\cdot (-15)=4+60=64,~~\sqrt{\Delta} =8\\\\[/tex]
[tex]x_{1} =\dfrac{-2-8}{2} =-5~~\lor~~x_{2} =\dfrac{-2+8}{2} =3\\f(x)=(x+5)\cdot (x-3)\\\\D=R-\{ -5,~~3 \}\\\\\dfrac{x^{2} +x-6 }{x+5} \div \dfrac{x-2}{x^{2} +2x-15 } =\dfrac{x^{2} +x-6 }{x+5} \cdot \dfrac{ x^{2} +2x-15}{x-2 }=\dfrac{(x+3)\cdot (x-2)}{x+5} \cdot \dfrac{(x+5)\cdot (x-3)}{x-2} =(x-3)\cdot (x+3)=x^{2} -9[/tex]
