#### Expressions collection:

Simplify these algebraic expressions to a single term.

\(\dfrac{4}{x} - \dfrac{3}{x-2}\)

\(\dfrac{4x}{5} + \dfrac{8x}{15} - \dfrac{1}{2}\)

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

\(\dfrac{2x}{x-3} - \dfrac{x}{x+1} + \dfrac{6-10x}{(x-3)(x+1)}\)

#### Equations collection:

Solve each equation.

\(\dfrac{3}{x+3} - \dfrac{1}{x-4} + \dfrac{57}{(x+3)(x-4)} = 1\)

\(\dfrac{4x}{5} - \dfrac{52}{15} = \dfrac{8}{3x}\)

\(\dfrac{3x}{4} +\dfrac{2x^2}{5} = \dfrac{x}{2}\)

\(\dfrac{x^2 - 2x}{x - 4} = \dfrac{2x}{x - 4}\)

#### Inequalities collection:

Solve these inequalities.

\(\dfrac{3(x-1)}{4} < \dfrac{5x-1}{2}\)

\(\dfrac{4x-3}{2} - \dfrac{2x+2}{5} ≥0\)

\(\dfrac{5}{3} - \dfrac{1}{x} < \dfrac{3}{x}\)

\(\dfrac{5x+6}{x-2} ≤ 2\)

As you work through the problems, think about the following questions.

How can you check if your solutions are correct?

What approach do you use for each problem?

- Do you use similar or different approaches across the different collections?