Wykonaj działania,wynik przedstaw w jak najprostszej postaci a) [latex]frac{-3x}{5x-1} - frac{x^{4}-6x^{3}}{10x^{3}-2x^{2}}[/latex] b)  [latex]frac{1}{x-2} + frac{x}{(x-2)^{2}}[/latex]

[latex]a)\ zalozenia : \ 5x-1 eq 0\ 5x eq 1 \ x eq frac{1}{5}\ 10x^3-2x^2 eq 0 \ 2x^2(5x-1) eq 0 \ 2x^2 eq 0 \ x eq 0\ 5x-1 eq 0 \ x eq frac{1}{5}\ xinRe - {0,frac{1}{5}} \ [/latex] obliczenia : [latex]frac{-3x}{5x-1} - frac{x^4-6x^3}{10x^3-2x^2}\ =frac{-3x}{5x-1} - frac{x^2(x^2-6x)}{2x^2(5x-1)} = \ =frac{-3x}{5x-1} - frac{x^2-6x}{2(5x-1)} = \ [/latex] [latex]=frac{-3xcdot 2}{2(5x-1)} - frac{x^2-6x}{2(5x-1)} = \ =frac{-6x}{2(5x-1)} - frac{x^2-6x}{2(5x-1)}=\ =frac{-6x-(x^2-6x)}{2(5x-1)} = \ =frac{-6x - x^2 +6x}{2(5x-1)} = \ =frac{-x^2}{2(5x-1)}[/latex] b) założenia : [latex]x-2 eq 0\ x eq 2\ (x-2)^2 eq 0 \ x-2 eq 0 \ x eq 2\ xinRe - {2}[/latex] obliczenia : [latex]frac{1}{x-2} + frac{x}{(x-2)^2} = \ =frac{1(x-2)}{(x-2)^2 + frac{x}{(x-2)^2} = \ =frac{x-2}{(x-2)^2} + frac{x}{(x-2)^2} = \ =frac{x-2+x}{(x-2)^2} = \ =frac{2x-2}{(x-2)^2}[/latex]