6.8.1 - Test: Rational Expressions and Functions Unit Test Part 1

Answer 1

1. Simplify the following rational expression: \( \frac{3x^2 + 5x - 2}{x^2 - 4x - 5} \).

2. Find the domain of the rational function: \( \frac{x^2 + 3x - 10}{x^2 - 9x + 20} \).

3. Solve the rational equation: \( \frac{2x - 1}{x} = \frac{3}{x} \).

4. Determine the vertical asymptotes of the rational function: \( \frac{x^2 - 5x + 6}{x - 2} \).

5. Find the simplified form of the following complex fraction: \( \frac{\frac{1}{x} - \frac{1}{y}}{\frac{1}{x} + \frac{1}{y}} \).