Simplifying a Rational Expression and Where It Is Undefined Worksheet with Answer Key

What's on the worksheet

1. Find every excluded value for each rational expression, or say there is none.
   \dfrac{x + 2}{3x - 12}\dfrac{x^2 - 4}{x^2 + 6x}\dfrac{x - 4}{x^2 - 8x + 16}\dfrac{5}{2x^2 - 7x - 15}\dfrac{x + 1}{x^3 + x^2 - 4x - 4}
2. Simplify each expression and state the restrictions.
   \dfrac{12a^3b}{18ab^4}\dfrac{x^2 - 2x - 8}{x^2 + 2x}\dfrac{3x^2 - 2x - 8}{3x^2 + 7x + 4}\dfrac{x^4 - 1}{x^2 + x}\dfrac{x^2 + 5x + 6}{x^2 + 5x + 4}
3. Simplify, watching which factors are opposites, and state the restrictions.
   \dfrac{x + 8}{8 + x}\dfrac{4 - 3x}{3x - 4}\dfrac{(x - 6)^2}{(6 - x)(x + 1)}\dfrac{(2 - x)^3}{(x - 2)^2}\dfrac{x^2 - 9}{(3 - x)(-3 - x)}
4. Show with one value that Priya's cancellation is wrong and find the correct simplification.
5. Word problem: the ratio of surface area to volume of a box with a square base.
6. Decide for which real numbers each statement is true.