Respuesta :

mreijepatmat
(x² - 25) / (x2 - 3x - 10)

1) Expand the 1st factor: (x² - 25) = (x-5)(x+5)

2) factorize the 2nd: (x2 - 3x - 10), it's a quadratic equation with 5 & -2 as roots.
    Then (x2 - 3x - 10) = (x-5)(x+2)

3) replace the latter in (x² - 25) / (x2 - 3x - 10)

===>(x-5)(x+5) / (x-5)(x+2)==>after simplifying Numerator & Denominator we

will get :(x+5) / (x+2)




mjankiewicz
[tex]{\frac{x^2-25}{x^2-3x-10}=\frac{x^2-25}{x^2+2x-5x-10}=\frac{(x+5)(x-5)}{x(x+2)-5(x+2)}=\frac{(x+5)(x-5)}{(x+2)(x-5)}=\frac{x+5}{x+2}}[/tex]

domain
[tex]x\ne -2\ , \ x\ne 5\\\\ D: \ x \in \math R \backslash \{-2, 5\}[/tex]