Ulamki algebraiczne. Rownania wymierne. 1. Rozwiaz rownania: [latex]frac{3x-1}{x+2} - frac{2x+3}{x+2} = x-2[/latex] [latex] frac{ x^{2} + 1 }{x-3} + frac{-2x}{3-x} = 4x -12 [/latex] Z gory dziekuje.

[latex]frac{3x-1}{x+2}-frac{2x+3}{x+2}=x-2; D:x eq-2\\frac{3x-1-2x-3}{x+2}=x-2\\frac{x-4}{x+2}=x-2\\(x+2)(x-2)=x-4\\x^2-4=x-4\\x^2-x=-4+4\\x(x-1)=0\\x=0in D vee x=1in D[/latex] [latex]frac{x^2+1}{x-3}+frac{-2x}{3-x}=4x-12; D:x eq3\\frac{x^2+1}{x-3}+frac{-2x}{-(x-3)}=4x-12\\frac{x^2+1}{x-3}+frac{2x}{x-3}=4x-12\\frac{x^2+1+2x}{x-3}=4x-12\\x^2+2x+1=(x-3)(4x-12)\\x^2+2x+1=4x^2-24x+36\\x^2-4x^2+2x+24x+1-36=0[/latex] [latex]-3x^2+26x-35=0\\Delta=26^2-4cdot(-3)cdot(-35)=676-420=256; sqrtDelta=sqrt{256}=16\\x_1=frac{-26-16}{2cdot(-3)}=7in D vee x_2=frac{-26+16}{2cdot(-3)}=frac{5}{3}in D[/latex]