Evaluate $\frac{x^2-4}{x-2}$ at $x=3$, and confirm the value is allowed by the domain.

Is the expression $\frac{x^2+2x+1}{\sqrt{x}}$ a rational expression (i.e., a quotient of two polynomials)?

Simplify $\frac{x^3-x^2-6x}{x^2-4}$ and state any domain exclusions.

Which of the following denominators is already fully factored and is irreducible over the integer values?

Find the LCD of the denominators $45x$ and $12x^2$.

Compute the LCD for the denominators $9x$, $20x^2$, and $14$.

Simplify $\frac{3x-6}{x-2}$.

Simplify: $\frac{x^2-7x+10}{x^2-5x+6}$

Compute $\frac{x}{x^2-1}-\frac{2}{x+1}$.

Solve the rational equation $\frac{1}{6}+\frac{1}{x}=\frac{1}{4}$ for $x$.

Find the restrictions, if any, on $x$ for the equation $\frac{x-2}{x^2-5x+6}=\frac{1}{x-3}$.

Which of the following sequences is the correct and complete order of actions to solve a nontrivial rational equation with variable denominators?