\(\frac{x+4}{3}+\frac{x-5}{7}\)
\begin{align} & =\frac{7(x+4)+3(x-5)}{(3)(7)}\\
& =\frac{7x+28+3x-15}{21}\\
& =\frac{10x+13}{21}\end{align}
\(\frac{x+5}{2}-\frac{x-3}{4}\)
\begin{align} & =\frac{4(x+5)-2(x-3)}{(2)(4)}\\
& =\frac{4x+20-2x+6}{8}\\
& =\frac{2x+26}{8}\\
& =\frac{x+13}{4}\\
\end{align}
\(\frac{6}{2x+1}-\frac{x-1}{3}\)
\begin{align} & =\frac{3(6)-(2x+1)(x-1)}{(3)(2x+1)}\\
& =\frac{18-(2x^2-x-1)}{6x+3}\\
& =\frac{-2x^2+x+19}{6x+3}\\
\end{align}
\(\frac{x+1}{3x}-\frac{4x+6}{2x}\)
\begin{align} & =\frac{2x(x+1)-3x(4x+6)}{(3x)(2x)}\\
& =\frac{2x^2+2x-12x^2-18x}{6x^2}\\
& =\frac{-10x^2-16x}{6x^2}\\
& =\frac{-5x-8}{3x}\\
\end{align}