[latex]1.\frac{4}{2x^2+x}-frac{6x}{2x+1}=1 (*)\\D:2x^2+x eq0 wedge 2x+1 eq0\\2x(x+frac{1}{2}) eq0 wedge 2x eq-1\\x eq0 wedge x eq-frac{1}{2}\\(*) frac{4}{2x^2+x}-frac{6x^2}{2x^2+x}=1\\frac{4-6x^2}{2x^2+x}=1\\2x^2+x=4-6x^2[/latex] [latex]2x^2+6x^2+x-4=0\\8x^2+x-4=0\\Delta=1-4cdot8cdot(-4)=1+128=129; sqrtDelta=sqrt{129}\\x_1=frac{-1-sqrt{129}}{2cdot8}=-frac{1+sqrt{129}}{16}in D; x_2=-frac{1-sqrt{129}}{16}in D[/latex] [latex]2.\y=frac{x+5}{sqrt{frac{2x-3}{x+3}+2}}\\D:frac{2x-3}{x+3}+2 > 0\\frac{2x-3}{x+3}+frac{2(x+3)}{x+3} > 0 wedge x+3 eq0 o x eq-3\\frac{2x-3+2x+6}{x+3} > 0\\frac{4x+3}{x+3} > 0iff(4x+3)(x+3) > 0\\4x+3=0; x+3=0\\x=-frac{3}{4}; x=-3\\os pomocnicza w zalaczniku[/latex] [latex]xin(-infty;-3) cup (-frac{2}{3}; infty)\\\©DRK[/latex]
