\(\frac{3a^2-b^2}{a^2+b^2}=\frac{3\left(\frac{a}{b}\right)^2-1}{\left(\frac{a}{b}\right)^2+1}=\frac{3}{4}\Leftrightarrow4.3\left(\frac{a}{b}\right)^2-4=3.\left(\frac{a}{b}\right)^2+3\)
\(\Leftrightarrow9.\left(\frac{a}{b}\right)^2=7\Leftrightarrow\left(\frac{a}{b}\right)^2=\frac{7}{9}\Leftrightarrow\int^{\frac{a}{b}=\frac{\sqrt{7}}{3}}_{\frac{a}{b}=-\frac{\sqrt{7}}{3}}\)