a)[tex] \frac{5x(x-1)}{2x( x^{2} -2x+1)} = \frac{5x(x-1)}{2x(x-1) ^{2} } = \frac{5}{2(x-1)} [/tex]
b)[tex] \frac{ x^{2} -2x-3x+6}{ x^{2} -2x-4x+8} = \frac{x(x-2)-3(x-2)}{x(x-2)-4(x-2)} = \frac{(x-2)(x-3)}{(x-2)(x-4)} = \frac{x-3}{x-4} [/tex]
c)[tex] \frac{x( x^{2} -9)}{x( x^{2} -4x+3)}= \frac{x(x-3)(x+3)}{x( x^{2} -x-3x+3)} = \frac{x(x-3)(x+3)}{x[x(x-1)-3(x-1)]} = \frac{x(x-3)(x+3)}{x(x-1)(x-3)} = \frac{x+3}{x-1} [/tex]
d)[tex] \frac{ x^{2} (x-2)-9(x-2)}{x( x^{2} -5x+6)} = \frac{(x-2)( x^{2} -9)}{x( x^{2} -2x-3x+6)} = \frac{(x-2)(x-3)(x+3)}{x[x(x-2)-3(x-2)]} = \frac{(x-2)(x-3)(x+3)}{x(x-2)(x-3)} = \\ \frac{x-3}{x} [/tex]
