Răspuns:
Explicație pas cu pas:
[tex]E(x)=[\frac{x-6}{x^{2} -25} +\frac{x^{2} }{x^{2} -5x} -\frac{2x-2}{x+5} :(x-1)]:\frac{2x^{2} +x-6}{x^{2} -25}[/tex]
[tex]E(x)=[\frac{x-6}{(x-5)(x+5)} +\frac{x^{2} }{x(x-5)} -\frac{2(x-1)}{(x+5)(x-1)} ]:\frac{2x^{2} -8+x+2}{(x-5)(x+5)}[/tex]
[tex]E(x)=[\frac{x-6}{(x-5)(x+5)} +\frac{x }{(x-5)} -\frac{2}{(x+5)} ]:\frac{2(x-2)(x+2)+(x+2)}{(x-5)(x+5)}[/tex]
in paranteza aducem la acelasi numitor comun si vom avea aceeasi linie de fractie. Numitorul va fi (x-5)(x+5)
pe a doua amplificam cu x+5 si pe a treia cu x-5
[tex]E(x)=\frac{x-6+x^{2} +5x-2x+10}{(x-5)(x+5)} :\frac{(x+2)(2x-3)}{(x-5)(x+5)}[/tex]
[tex]E(x)=\frac{x^{2} +4x+4}{(x-5)(x+5)} \cdot \frac{(x-5)(x+5)}{(x+2)(2x-3)}[/tex]
[tex]E(x)=\frac{(x+2)^{2} }{(x-5)(x+5)} \cdot \frac{(x-5)(x+5)}{(x+2)(2x-3)}[/tex][tex]E(x)=\frac{x+2}{2x-3}[/tex]
