Zad. 3
[tex]b) \\\\\frac{2}{x+2}-\frac{1}{x-3}=0\\\frac{2}{x+2}=\frac{1}{x-3}\\2(x-3)=x+2\\2x-6=x+2\\2x-x=2+6\\x=8[/tex]
[tex]f)\\\\\frac{x+4}{2x-1}-\frac{1}{x}=0\\\frac{x+4}{2x-1}=\frac{1}x\\x(x+4)=2x-1\\x^2+4x=2x-1\\x^2+4x-2x+1=0\\x^2+2x+1=0\\\Delta=2^2-4*1*1=4-4=0\\x_0=\frac{-2}2=-1[/tex]
Zad. 4
[tex]c) \\\\x+1=\frac{2-2x}{x-1} /*(x-1)\\(x+1)(x-1)=2-2x\\x^2-1=2-2x\\x^2+2x-1-2=0\\x^2+2x-3=0\\\Delta=2^2-4*1*(-3)=4+12=16\\\sqrt{\Delta}=4\\x_1=\frac{-2-4}2=\frac{-6}2=-3\\x_2=\frac{-2+4}2=\frac22=1[/tex]
[tex]e)\\\\\frac{6x-4}{2-3x}=-2x /*(2-3x)\\6x-4=-2x(2-3x)\\6x-4=-4x+6x^2\\-6x^2+6x+4x-4=0\\-6x^2+10x-4=0\\\Delta=10^2-4*(-6)*(-4)\\\Delta=100-96\\\Delta=4\\\sqrt{\Delta}=2\\x_1\frac{-10-2}{-12}=\frac{-12}{-12}=1\\x_2=\frac{-10+2}{-12}=\frac{-8}{-12}=\frac23[/tex]
