Encontremos [tex]f(a+b)[/tex] substituindo [tex]a+b[/tex] em [tex]x[/tex], veja:
[tex]f(x)=x^2\\\\f(a+b)=(a+b)^2\\\\\boxed{f(a+b)=a^2+2ab+b^2}[/tex]
Raciocínio análogo para encontrar [tex]f(a-b)[/tex], segue,
[tex]f(x)=x^2\\\\f(a-b)=(a-b)^2\\\\\boxed{f(a-b)=a^2-2ab+b^2}[/tex]
Portanto,
[tex]\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}}[/tex]
