Rational Expressions, Equations, and Functions Worksheet
This worksheet covers simplifying rational expressions, solving rational equations, and understanding rational functions for Grade 9 Math.
Includes
Standards
Topics
Rational Expressions, Equations, and Functions
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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 \( \frac{2x+4}{x^2-4} \times \frac{x-2}{6} \)?
\( \frac{1}{3} \)
\( \frac{1}{3x} \)
\( \frac{x-2}{3(x+2)} \)
\( \frac{x+2}{3} \)
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.
True
False
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.
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