Question

Expressões algébricas. em anexo.

Answer 1

1) Observe que, $2x^2+4x-8=2(x^2+2x-4)$. Assim:

$\dfrac{2x^2+4x-8}{x^2+2x-4}=\dfrac{2(x^2+2x-4)}{(x^2+2x-4)}=2$.



2) Note que, $2x^2-6x=2x(x-3)$. Deste modo:

$\dfrac{2x^2-6x}{x-3}=\dfrac{2x(x-3)}{(x-3)}=2x$.




3) Veja que, $5m^2+10m+5=5(m+1)^2=5(m+1)(m+1)$.

Assim, $\dfrac{m^2+m}{5m^2+10m+5}=\dfrac{m(m+1)}{5(m+1)(m+1)}=\dfrac{m}{5(m+1)}$.



4) Temos que, 

$a^2+6a+9=a^2+3a+3a+9=a(a+3)+3(a+3)=(a+3)(a+3)$.

$a^2-9=a^2-3^2=(a+3)(a-3)$


Logo, $\dfrac{a^2-9}{a-3}=\dfrac{(a+3)(a-3)}{(a-3)}=a+3$.

E

$\dfrac{a^2+6a+9}{3}\div\dfrac{a^2-9}{a-3}=\dfrac{a^2+6a+9}{3}\div(a+3)=\dfrac{(a+3)(a+3)}{3(a+3)}=\dfrac{(a+3)}{3}$.