f(x)=\frac{4x^2 + 8x+ 13}{6(x+1)}=\frac{4\cdot (x^2 + 2x+ 1)+9}{6\cdot (x+1)}=\frac{2}{3}\cdot (x+1)+\frac{1}{\frac{2}{3}\cdot (x+1)}=t+\frac{1}{t}