\(\textbf{Zadatak 2.}\) Skrati razlomak

\begin{equation*}
\frac{2x^{2}+5x-3}{3x^{2}+11x+6}
\end{equation*}

\(\textbf{Rješenje:)}\\ \textbf{a)}\)

\begin{equation*}
2x^{2}+5x-3=0\\ 
x_{1,2}=\frac{-5\pm 7}{4}\\
x_{1}=-3;\:\: x_{2}=\dfrac{1}{2}
\end{equation*}

\(\textbf{b)}\\\)

\begin{equation*}
3x^{2}+11x+6=0\\
x_{1,2}=\frac{-11\pm 7}{6}\\
x_{1}=-3;\:\: x_{2}=-\dfrac{2}{3}
\end{equation*}

Konačno iz a) i b) slijedi:

\\begin{equation*}
\frac{2x^{2}+5x-3}{-3x^{2}+11x+6}=\dfrac{2\left( x+3\right) \left( x-\dfrac{1}{2}\right) }{3\left( x+3\right) \left( x+\dfrac{2}{3}\right) }\\=\dfrac{2x-1}{3x+2}\end{equation*}