Rational Expressions, Equations, and Functions Worksheet

Rational Expressions, Equations, and Functions

Read each question carefully and provide the best answer. Show all your work for full credit.

1. Simplify the following rational expression, stating any restrictions on the variable:

\( \frac{x^2 - 9}{x^2 + 5x + 6} \)

2. Which of the following is equivalent to \( \frac{2x+4}{x^2-4} \times \frac{x-2}{6} \)?

3. To add or subtract rational expressions, you must first find a   to combine them.

4. The simplified sum of \( \frac{3}{x+1} + \frac{2}{x-1} \) is  .

5. Solve the following rational equation for x, checking for extraneous solutions:

\( \frac{1}{x} + \frac{1}{2} = \frac{3}{4} \)

6. A rational function can have a vertical asymptote where its denominator is zero.

7. For the function \( f(x) = \frac{1}{x-3} \), identify the vertical and horizontal asymptotes.

8. Sketch the graph of \( f(x) = \frac{1}{x-3} \) on the coordinate plane below, labeling the asymptotes.