Rational Expressions and Functions

Remembering: Match the following vocabulary to the definitions.

Remembering: List the steps to simplify the following rational expression

$$\frac{x^2-x-6}{x+3}+\frac{4}{x-2}$$

Understanding: How would you explain why an asymptote occurs on a rational equation?

Understanding: A student was asked to identify the domain and range of a rational function. The student identified the domain as $$\left(-\infty,2\right)\cup\left(2,\infty\right)$$ . Interpret what the domain represents.

Applying: The area of a rectangular room is given as $$\frac{5}{x+4}$$ . If the length of the room is $$\frac{25x+30}{35x+42}$$ . Calculate the width of the room.

Applying: Solve the following rational equation and select the real solution.

$$\frac{1}{r-2}+\frac{1}{r^2-7r+10}=\frac{6}{r-2}$$

Analyzing: Compare and contrast the graphs of the following two rational expressions.

Analyzing: How does changing (x-5) into (x+3) affect the graph following rational expression?

$$\frac{x^2+8x+12}{x-5}$$