[latex]Sprowadz wyrazenia do wspolnego mianownika 2x-1 dzielone przez 3x do kwadratu + 2x -1 drugi ulamek to x+1 przez 6x do kwadratu -5x+1 \ frac{2x- frac{2x-1}{3x^2+2x-1}+frac{x+1}{6x^2-5x+1} =frac{2x-1}{3(x+1)(x-frac{1}{3})}+frac{x+1}{6(x-frac{1}{3})(x-frac{1}{2})}=} \ [/latex] [latex]=frac{(x-frac{1}{2})(12x-6)}{6(x-frac{1}{2})(x+1)(x-frac{1}{3})}+frac{(x+1)(x+1)}{6(x-frac{1}{3})(x-frac{1}{2})(x+1)} = [/latex] [latex]=frac{(x-frac{1}{2})(12x-6)}{6(x-frac{1}{2})(x+1)(x-frac{1}{3})}+frac{(x+1)(x+1)}{6(x-frac{1}{3})(x-frac{1}{2})(x+1)} \ =frac{(x-frac{1}{2})(12x-6)+(x+1)^2}{6(x-frac{1}{2})(x-frac{1}{3})(x+1)}[/latex] [latex]=frac{(x-frac{1}{2})(12x-6)+(x+1)^2}{6(x-frac{1}{2})(x-frac{1}{3})(x+1)}=frac{12x^2-6x-6x+3+x^2+2x+1}{(6x-3)(x^2+x-frac{1}{3}x-frac{1}{3})}=[/latex] [latex]=frac{12x^2-6x-6x+3+x^2+2x+1}{(6x-3)(x^2+x-frac{1}{3}x-frac{1}{3})}= frac{13x^2-10x+4}{6x^3+18x^2-2x^2-2x-3x^2-3x+x+1}= \ =frac{13x^2-10x+4}{6x^3+13x^2-4x+1}[/latex]
