Add and subtract rational expressions, and simplify complex fractions

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Jun works out x/(x − 3) + 4/(x − 3) on a worksheet. Which is the answer in simplest form?

   • (x + 4)/(x − 3)
   • 4x/(x − 3)
   • (x + 4)/(2x − 6)
2. 2.

   Kira works out 2x/(x + 5) + 3/(x + 5) in a notebook. Which is the answer in simplest form?

   • (2x + 3)/(x + 5)
   • (2x + 3)/(2x + 10)
   • 6x/(x + 5)
3. 3.

   Luz works out (2x + 1)/(x + 4) − (x − 3)/(x + 4) in pencil. Which is the answer in simplest form?

   • (x − 2)/(x + 4)
   • 1
   • (3x − 2)/(x + 4)
4. 4.

   Milo works out (3x + 2)/(x − 1) − (x + 6)/(x − 1) from a math book. Which is the answer in simplest form?

   • (4x + 8)/(x − 1)
   • (2x + 8)/(x − 1)
   • (2x − 4)/(x − 1)
5. 5.

   Noah adds 1/((x + 1)(x − 4)) + 3/((x − 4)(x + 2)) on a worksheet. Which is the least common denominator (LCD)?

   • (x + 1)(x − 4)²(x + 2)
   • (x + 1)(x − 4)(x + 2)
   • x − 4
6. 6.

   Ren adds 4/((x − 2)(x + 5)) + x/((x + 5)(x − 6)) in pencil. Which is the least common denominator (LCD)?

   • (x − 2)(x + 5)(x − 6)
   • (x − 2)(x + 5)²(x − 6)
   • x + 5
7. 7.

   Zee writes 3/(x + 2) + 2/(x − 1) over the bottom (x + 2)(x − 1) on a worksheet. What is the top, multiplied out and combined?

   5x + 1
8. 8.

   Ari writes 4/(x − 3) + 1/(x + 5) over the bottom (x − 3)(x + 5) in a notebook. What is the top, multiplied out and combined?

   5x + 17
9. 9.

   Bo writes 5/(x + 1) − 2/(x + 4) over the bottom (x + 1)(x + 4) in pencil. What is the top, multiplied out and combined?

   3x + 18
10. 10.

    Esme writes 6/(x − 2) − 3/(x + 3) over the bottom (x − 2)(x + 3) from a math book. What is the top, multiplied out and combined?

    3x + 24