\(\dfrac{3x}{5} + \dfrac{x}{4}\)

$$\begin{align}
& \dfrac{3x}{5} + \dfrac{x}{4} \\[0.5em]
=\ & \dfrac{12x}{20} + \dfrac{5x}{20} \\[0.5em]
=\ & \dfrac{17x}{20}
\end{align}$$

\(\dfrac{2x}{3} - \dfrac{x}{5}\)

$$\begin{align}
& \dfrac{2x}{3} - \dfrac{x}{5} \\[0.5em]
=\ & \dfrac{10x}{15} - \dfrac{3x}{15} \\[0.5em]
=\ & \dfrac{7x}{15}
\end{align}$$

\(\dfrac{2x - 3}{7} + \dfrac{x + 4}{5}\)

$$\begin{align}
& \dfrac{2x - 3}{7} + \dfrac{x + 4}{5} \\[0.5em]
=\ & \dfrac{10x - 15}{35} + \dfrac{7x + 28}{35} \\[0.5em]
=\ & \dfrac{17x + 13}{35}
\end{align}$$

\(\dfrac{3(x - 1)}{4} - \dfrac{2(x + 6)}{9}\)

\(\dfrac{6}{1 - 2x} - \dfrac{5}{x - 4}\)

\(\dfrac{3x - 3}{x^2 - x} - \dfrac{x^2 - 3x}{x^3 - x^2}\)

\(\dfrac{1}{x - 1} + \dfrac{1}{3x} - \dfrac{1}{x^2(x - 1)}\)

\(\dfrac{x^2 - 39}{x^2 + 3x - 10} - \dfrac{x - 7}{x - 2}\)

\(\dfrac{4x + 3}{x^2 - 9} - \dfrac{x + 1}{x - 3}\)

\(\dfrac{4}{x} + \dfrac{7}{5x^2} - \dfrac{10}{4x}\)

\(\dfrac{x}{2x^2 - 5x + 3} - \dfrac{2x}{2x^2 - x - 3}\)

\(\dfrac{6}{b - 6} + \dfrac{4}{b - 8}\)

\(\dfrac{2}{x + 3} + \dfrac{1}{x + 5}\)

\(\dfrac{2a}{a - 3} - \dfrac{2a}{a + 3} + \dfrac{36}{a^2 - 9}\)

\(\dfrac{y - 5}{y^2 - 3y - 10} + \dfrac{y}{y^2 + y - 2}\)

\(\dfrac{5}{x + 1} - \dfrac{3}{x + 2}\)

\(\dfrac{x + 3}{x^2 - 25} - \dfrac{x - 1}{x - 5} + \dfrac{3}{x + 3}\)

\(\dfrac{1}{x + 4} + \dfrac{1}{x + 5}\)

\(\dfrac{1 - 3x}{x - 6} + \dfrac{2}{2x + 1}\)

\(\dfrac{-4x^2 + 2}{x^2 + 9x - 10} + \dfrac{3}{x + 10}\)