Explicație pas cu pas:
1.
a)
[tex]\frac{2x+3}{x-4} *\frac{x-1}{x+4} =\frac{(2x+3)*(x-1)}{(x-4)*(x+4)} =\frac{2x^{2} -2x+3x-3}{x^{2} -4^{2} } =\frac{2x^{2} +x-3}{x^{2} -16 }[/tex]
b)
[tex]\frac{x+3}{x-5} *\frac{x+3}{1-4x} =\frac{(x+3)^{2} }{(x-5)*(1-4x)} =\frac{(x+3)^{2} }{x-4x^{2} -5+20x}=\frac{x^{2} +6x+9}{-4x^{2} +21x-5}[/tex]
2.
[tex]\frac{2x^{2} +4x+2}{6x^{4} -12x^{3} } *\frac{3x^{2} }{x+1} -\frac{x+4}{x^{2} -4} =\frac{2(x^{2} +2x+1)}{6x^{3}(x -2)} *\frac{3x^{2} }{x+1} -\frac{x+4}{(x-2)(x+2)} =[/tex]
[tex]=\frac{2(x+1)^{2} }{2x(x -2)} *\frac{1}{x+1} -\frac{x+4}{(x-2)(x+2)} =\frac{x+1}{x(x -2)} -\frac{x+4}{(x-2)(x+2)} =\frac{(x+1)(x+2)-x(x+4)}{x(x-2)(x+2)} =[/tex]
[tex]=\frac{x^{2} +2x+x+2-x^{2} -4x}{x(x+2)(x-2)} =\frac{2-x}{x(x+2)(x-2)} =-\frac{1}{x(x+2)}[/tex]
