zaznacz na osi liczbowej zbiór rozwiązań nierównośći x-3÷x-4≤x-1÷x-3

[latex]D: xin R- {3,4}[/latex] [latex]frac{x-3}{x-4}le frac{x-1}{x-3}[/latex] [latex]frac{x-1}{x-3}-frac{x-3}{x-4}ge0[/latex] [latex]frac{(x-1)(x-4)-(x-3)^{2}}{(x03)(x-4)}ge0[/latex] [latex]frac{x^{2}-5x+4-(x^{2}-6x+9)}{x^{2}-7x+12}ge0[/latex] [latex]frac{x-5}{x^{2}-7x+12}ge0Leftrightarrow(x-5ge0wedge x^{2}-7x+12ge0)[/latex] [latex]vee(x-5<0 wedge x^{2}-7x+12<0)[/latex] [latex]x^{2}-7x+12[/latex] [latex]Delta=(-7)^{2}-4cdot 12=49-48=1[/latex] [latex]x_{1}=frac{7-1}{2}=3[/latex] [latex]x_{2}=frac{7+1}{2}=4[/latex] [latex] x^{2}-7x+12ge0Leftrightarrow xin(-infty;3>cup <4;+infty)[/latex] [latex] x^{2}-7x+12<0Leftrightarrow xin (3;4)[/latex] 1. rozwiązanie; [latex]x-5ge0 wedge x^{2}-7x+12ge0[/latex] [latex]xge5 wedge xin(-infty ; 3>cup <4;+infty )[/latex] [latex]xin<5;+infty)[/latex] 2. rozwiązanie: [latex]x-5<0 wedge x^{2}-7x+12<0[/latex] [latex]x<5 wedge xin(3;4)[/latex] [latex]xin(3;4)[/latex] ostatecznie: [latex]xin(3;4)cup <5;+infty )[/latex]