Zad. 8
[tex]a) \\\\\frac{x-2}{x^2}*\frac{3x}{2x-4}=\frac{x-2}x*\frac3{2(x-2)}=\frac{1}x*\frac32=\frac3{2x}[/tex]
[tex]b) \\\frac{3x+4.5}{x-1}*\frac{1-x}{x+1,5}=\frac{1.5(2x+3)}{x-1}*\frac{-1(-1+x)}{0.5(2x+3)}=\frac{3}{x-1}*\frac{-(x-1)}{1}=\frac{-3}1=-3[/tex]
[tex]c) \\\frac{x^2}{3-x}*\frac{3x-9}{x^2}=\frac{1}{-(-3+x)}*\frac{3(x-3)}{x^2}=\frac{1}{-(x-3)}*\frac{3(x-3)}{x^2}=-1*\frac3{x^2}=-\frac{3}{x^2}[/tex]
[tex]d) \\\frac{x-1}{x+1}*\frac{x^3+x^2}{x^4-1}=\frac{x-1}{x+1}*\frac{x^2(x+1)}{(x-1)(x+1)(x^2+1)}=\frac11*\frac{x^2}{(x+1)(x^2+1)}=\frac{x^2}{(x+1)(x^2+1)}[/tex]
[tex]e) \\\frac{x-\frac12}{x^2-1}*\frac{(x+1)^2}{2x-1}=\frac{x-\frac12}{x-1}*\frac{x+1}{2(x-\frac12)}=\frac{1}{x-1}*\frac{x+1}2=\frac{x+1}{2(x-1)}=\frac{x+1}{2x-2}[/tex]
[tex]f) \\\frac{x^2-4}{x^3+3x^2}*\frac{x^4-9x^2}{x^2+2x}=\frac{(x-2)(x+2)}{x^2(x+3)}*\frac{x^2(x-3)(x+3)}{x(x+2)}=\frac{x-2}{1}*\frac{x-3}{x}=\frac{(x-2)(x-3)}x[/tex]
