Identify the numerator and denominator in the expression $\frac{3x^2+1}{x-4}$.

Simplify the expression $\frac{4x^3}{6x^2}$.

Simplify the rational expression $\frac{x^2-9}{x^2-6x+9}$ and state any domain restrictions.

If a rational expression has a common factor (x + 1) that cancels in simplification, must x = -1 be excluded from the simplified expression's domain?

Simplify $\frac{x^2-5x+6}{x^2-4}\cdot \frac{x+2}{x-3}$ and state any excluded $x$-values.