Simplify $\frac{x^5}{x^2}$, assuming $x\ne 0$.

Simplify $\frac{x+5}{2x+10}$ by factoring out the greatest common factor, and state any excluded value.

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?

Factor the numerical denominators $84$ and $36$ completely into prime factors, then find the LCD of $\frac{1}{84}$ and $\frac{1}{36}$.

Rewrite the pair of rational expressions $\frac{1}{30x}$ and $\frac{1}{20x^2}$ so both have the LCD $60x^2$.

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

Given $\frac{5}{x+3}-\frac{2}{x-1}$, form a single rational expression, expand and combine terms, and present the simplified numerator.

Compute $\frac{1}{2x}+\frac{3}{x+1}$.

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

Solve the following rational equation for $x$:

$\frac{1}{x^2-5x+6}+\frac{1}{x-2}=\frac{1}{x+3}$

Which justification best explains why multiplying both sides of a rational equation by the LCD is a valid step when solving rational equations (provided you track restrictions)?