Question

    F(a+b) - f(a-b)
______________ sendo f(x)= x² e ab ≠0
              ab


a outra é 
   F(a+b) - f(a-b)
______________ sendo f(x)=3x+1 e ab ≠0
              ab

Answer 1

Encontremos $f(a+b)$ substituindo $a+b$ em $x$, veja:

$f(x)=x^2\\\\f(a+b)=(a+b)^2\\\\\boxed{f(a+b)=a^2+2ab+b^2}$


 Raciocínio análogo para encontrar $f(a-b)$, segue,

$f(x)=x^2\\\\f(a-b)=(a-b)^2\\\\\boxed{f(a-b)=a^2-2ab+b^2}$

 Portanto,

$\frac{f(a+b)-f(a-b)}{ab}=\\\\\\\frac{a^2+2ab+b^2-(a^2-2ab+b^2)}{ab}=\\\\\\\frac{a^2+2ab+b^2-a^2+2ab-b^2}{ab}=\\\\\\\frac{4ab}{ab}\\\\\\\boxed{\boxed{4}}$