Question 1: Simplify the algebraic fraction \( \frac{3x}{4} + \frac{2x}{4} \).

Answer: x

Question 2: Calculate \( \frac{2a}{3} \times \frac{3b}{4} \).

Answer: \frac{ab}{2}

Question 3: Divide \( \frac{6x^2}{5} \) by \( \frac{3x}{2} \).

Answer: \frac{4x}{5}

Question 4: Add \( \frac{5m}{6} \) and \( \frac{2m}{3} \).

Answer: \frac{9m}{6} or \frac{3m}{2}

Question 5: Construct a simplified algebraic fraction for \( \frac{4x^2 - 9}{2x + 3} \).

Answer: \frac{(2x - 3)(2x + 3)}{2x + 3} = 2x - 3

Question 6: Solve for x: \( \frac{x+2}{x-1} = \frac{3}{2} \).

Answer: x=7

Question 7: A calculator shows the result of \( \frac{3x}{4} - \frac{x}{2} \) as 0.75. Find the value of x.

Answer: x=1

Question 8: Express \( \frac{2x}{3} + \frac{4x}{5} \) as a single fraction.

Answer: \frac{22x}{15}

Question 9: Multiply \( \frac{a+1}{a-1} \) by \( \frac{a-1}{a+2} \).

Answer: \frac{a+1}{a+2}

Question 10: Identify and correct the mistake in simplifying: \( \frac{3x}{6} + \frac{2x}{4} = \frac{5x}{6} \).

Answer: The second fraction should be \( \frac{2x}{4} = \frac{x}{2} \). When adding, common denominator is 4, so sum is \( \frac{2x}{4} + \frac{2x}{4} = \frac{4x}{4} = x \).

Question 11: Challenge: Simplify \( \frac{4x^2 - 25}{2x + 5} \).

Answer: 2x - 5