Rational Expressions Quiz

Grade 11 · Math · Quiz

10 questions on simplifying, multiplying, dividing, and adding rational expressions.

Questions

1. Simplify: (6x²)/(3x).

   1. 2
   2. 2x
   3. 3x
   4. 6x
   Show answer

   Answer: 2x

   6x²/(3x) = 2x.

2. What are the excluded values of (x−1)/((x+2)(x−3))?

   1. x = 2 and x = −3
   2. x = −2 and x = 3
   3. x = 1
   4. x = −1 and x = 3
   Show answer

   Answer: x = −2 and x = 3

   Set each denominator factor to zero: x+2=0 → x=−2; x−3=0 → x=3.

3. Simplify: (x² + 5x + 6)/(x + 2).

   1. x + 3
   2. x + 2
   3. x + 6
   4. x − 3
   Show answer

   Answer: x + 3

   Factor: (x+2)(x+3)/(x+2) = x+3.

4. Multiply: (3/x) · (x²/9).

   1. x/3
   2. 3x
   3. 1/3
   4. 9/x
   Show answer

   Answer: x/3

   3x²/(9x) = x/3.

5. Divide: (5/x²) ÷ (10/x).

   1. 50/x³
   2. 2/x
   3. 1/(2x)
   4. x/2
   Show answer

   Answer: 1/(2x)

   (5/x²) · (x/10) = 5x/(10x²) = 1/(2x).

6. Subtract: 3/(x+1) − 1/(x+1).

   1. 2/(x+1)
   2. 4/(x+1)²
   3. 2
   4. 2/(2x+2)
   Show answer

   Answer: 2/(x+1)

   Same denominator: (3−1)/(x+1) = 2/(x+1).

7. Which is the LCD for 1/x + 1/(x+3)?

   1. x
   2. x+3
   3. x(x+3)
   4. x + (x+3)
   Show answer

   Answer: x(x+3)

   The LCD of different denominators x and (x+3) is their product x(x+3).

8. Simplify: (x² − 16)/(x − 4).

   1. x − 4
   2. x + 4
   3. x + 16
   4. (x+4)(x−4)
   Show answer

   Answer: x + 4

   x²−16 = (x+4)(x−4); cancel (x−4) to get x+4 (where x ≠ 4).

9. Add and simplify: 2/(x−1) + 3/(x+1).

   1. 5/(x²−1)
   2. (5x−1)/(x²−1)
   3. (5x+5)/(x²−1)
   4. (5x+1)/(x²−1)
   Show answer

   Answer: (5x−1)/(x²−1)

   LCD = (x−1)(x+1). Numerator: 2(x+1) + 3(x−1) = 2x+2+3x−3 = 5x−1.

10. Simplify the complex fraction: (1/2)/(3/4).

    1. 3/8
    2. 2/3
    3. 6/4
    4. 4/6
    Show answer

    Answer: 2/3

    (1/2) ÷ (3/4) = (1/2) · (4/3) = 4/6 = 2/3.

Get a personalized course on Rational Expressions built around your child.