Question

$\frac{ a^{3} - 8^{2}+ 16a }{ a^{2}-16 } . \frac{a+4}{a}$
E calcule o seu valor numerico para " a=104"

Answer 1

$\frac{a(a^2-8a+16)}{a^2-16}\cdot\frac{a+4}{a}=\\\\\\\frac{a(a-4)^2}{(a+4)(a-4)}\cdot\frac{a+4}{a}=\\\\\\\frac{a(a+4)(a-4)^2}{a(a+4)(a-4)}=\\\\a-4=\\\\104-4=\\\\\boxed{100}$

Answer 2

Veja que:

$\rhd$ $a^3-8a^2+16a=a(a^2-8a+16)=a(a-4)^2$

$\rhd$ $a^2-16=(a+4)(a-4)$

Assim:

$\dfrac{a^3-8a^2+16a}{a^2-16}\cdot\dfrac{a+4}{a}=\dfrac{a(a-4)^2\cdot(a+4)}{(a+4)(a-4)\cdot a}=a-4$.

Se $a=104$, temos que:

$\dfrac{a^3-8a^2+16a}{a^2-16}\cdot\dfrac{a+4}{a}=a-4=104-4=100$