Question

Se f(x)=$\frac{x+a}{x-a}$ , então $\frac{f(a+3)}{f(a-3)}$ é igual a
a) $\frac{a^{2}+2a+3 }{ -a^{2}+4a+3 }$
b)$\frac{3+2a}{3+a}$
c)$\frac{3+2a}{3}$
d)$\frac{3+2a}{2a-3}$
e)$\frac{3+2a}{3-2a}$

Answer 1

$f(x)=\dfrac{x+a}{x-a}$

$f(a+3)=\dfrac{a+3+a}{a+3-a}=\dfrac{2a+3}{3}$

$f(a-3)=\dfrac{a-3+a}{a-3-a}=\dfrac{2a-3}{-3}$

Logo:

$\dfrac{f(a+3)}{f(a-3)}=\dfrac{\dfrac{2a+3}{3}}{\dfrac{2a-3}{-3}}=\dfrac{2a+3}{3}\cdot\dfrac{-3}{2a-3}$

$\dfrac{f(a+3)}{f(a-3)}=\dfrac{-2a-3\cdot(-1)}{2a-3\cdot(-1)}=\dfrac{3+2a}{3-2a}$

Alternativa E