\(\frac{4x+x^2}{8x}\)

\begin{align} & =\frac{x(4+x)}{8x}\\ & =\frac{4+x}{8}\end{align}

\(\frac{6xy-12x^2}{2xy}\)

\begin{align} & =\frac{6x(y-2x)}{2xy}\\ & =\frac{3(y-2x)}{y}\end{align}

\(\frac{y^2+y}{y^2-1}\)

\begin{align} & =\frac{y(y+1)}{(y+1)(y-1)}\\ & =\frac{y}{y-1}\end{align}

\(\frac{f^2+f-6}{f^2-f-2}\)

\begin{align} & =\frac{(f+3)(f-2)}{(f+1)(f-2)}\\ & =\frac{f+3}{f+1}\end{align}