Odpowiedź:
A.
[tex]\frac{4x^{2} +2}{x^{3}} -5+\frac{4x}{x^{2} } = \frac{4x^{2} +2}{x^{3}} *\frac{x^3}{x^3} -5 *\frac{x^6}{x^6} +\frac{4x}{x^2} *\frac{x^4}{x^4} =\frac{(4x^{2} +2)*x^3}{x^{6}} -\frac{5x^6}{x^6} +\frac{4x*x^4}{x^6} =\\=\frac{4x^{5} +2x^3}{x^{6}}-\frac{5x^6}{x^6} +\frac{4x^5}{x^6} =\frac{4x^5+2x^3-5x^6+4x^5}{x^6} =\frac{-5x^6+2x^3}{x^6} =\frac{x^3(-5x^3+2)}{x^6} =\frac{-5x^3+2}{x^3}[/tex]
B.
[tex]\frac{x-5}{x} +2-\frac{4x^2}{x^3} =\frac{x-5}{x} *\frac{x^2}{x^2} +2*\frac{x^3}{x^3} -\frac{4x^2}{x^3}=\frac{(x-5)*x^2}{x^{1+2} } +\frac{2x^3}{x^3} -\frac{4x^2}{x^3}=\\=\frac{(x^3-5x^2)}{x^{3} }+\frac{2x^3-4x^2}{x^3}=\frac{x^3-5x^2+2x^3-4x^2}{x^3} =\frac{3x^2-9x^3}{x^3} = \frac{x^2(3-9x)}{x^3}=\frac{(3-9x)}{x}[/tex]
C.
[tex]\frac{x^2}{x^4} +2-\frac{4x}{x^4} =\frac{x^2}{x^4} +2*\frac{x^4}{x^4}- \frac{4x}{x^4}=\frac{x^2}{x^4}+\frac{2x^4}{x^4}- \frac{4x}{x^4}=\frac{x^2+2x^4-4x}{x^4} =\\=\frac{x(x+2x^3-4)}{x^4}=\frac{x+2x^2-4}{x^3}=\frac{2x^2+x-4}{x^3}[/tex]
Szczegółowe wyjaśnienie:
