[latex]frac{x^{3}+3x^{2}-10x}{x^{5}-5x^{4}+6x^{3}}= frac{x(x^{2}+3x-10)}{x^{3}(x^{2}-5x+6)}= frac{x(x+5)(x-2)}{x^{3}(x-2)(x-3)}= frac{x+5}{x^{2}(x-3)} [/latex] [latex]x^{2}+3x-10=(x+5)(x-2)\ Delta=b^{2}-4ac=3^{2}-4*1*(-10)=9+40=49\ sqrt{Delta}=7\ \ x_{1}=frac{-b-sqrt{Delta}}{2a}=frac{-3-7}{2}=frac{-10}{2}=-5\ \ x_{2}=frac{-b+sqrt{Delta}}{2a}=frac{-3+7}{2}=frac{4}{2}=2\[/latex] [latex]x^{2}-5x+6=(x-2)(x-3)\ Delta=b^{2}-4ac=(-5)^{2}-4*1*6=25-24=1\ sqrt{Delta}=1\ \ x_{1}=frac{-b-sqrt{Delta}}{2a}=frac{5-1}{2}=frac{4}{2}=2\ \ x_{2}=frac{-b+sqrt{Delta}}{2a}=frac{5+1}{2}=frac{6}{2}=3\[/latex]
Uprość wyrażenie (wyjaśnić przy okazji proszę): [latex]frac{1}{2x^2+5x} - frac{2}{25-10x}-frac{4}{4x^2-25}[/latex]...
