Add and subtract rational expressions, and simplify complex fractions

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Jun works out x/(x² − 25) − 1/(x − 5) on a worksheet. Which is the answer as one fraction?

   • (2x + 5)/((x − 5)(x + 5))
   • -5/((x − 5)(x + 5))
   • 5/((x − 5)(x + 5))
   • (x − 1)/((x − 5)(x + 5))
2. 2.

   Kira works out 3x/(x² − 9) − 2/(x − 3) in a notebook. Which is the answer as one fraction?

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

   Luz works out (x + 5)/(x² + 3x + 2) − 1/(x + 1) in pencil. Which is the answer as one fraction?

   • 7/((x + 1)(x + 2))
   • 3/((x + 1)(x + 2))
   • (x + 4)/((x + 1)(x + 2))
   • (2x + 7)/((x + 1)(x + 2))
4. 4.

   Milo works out 2x/(x² − x − 6) − 3/(x − 3) from a math book. Which is the answer as one fraction?

   • (2x − 3)/((x − 3)(x + 2))
   • (-x − 6)/((x − 3)(x + 2))
   • (5x + 6)/((x − 3)(x + 2))
   • (-x + 6)/((x − 3)(x + 2))
5. 5.

   Noah writes 2x/(x² − 9) + 3/(x − 3) over the bottom (x − 3)(x + 3) on a worksheet. What is the top, multiplied out and combined?

   5x + 9
6. 6.

   Pia writes 4/(x² − 1) + x/(x − 1) over the bottom (x − 1)(x + 1) in a notebook. What is the top, multiplied out and combined?

   x² + x + 4
7. 7.

   Ren writes 5x/(x² + 3x − 4) − 2/(x + 4) over the bottom (x + 4)(x − 1) in pencil. What is the top, multiplied out and combined?

   3x + 2
8. 8.

   Tala writes 3/(x² − 5x + 6) − 1/(x − 2) over the bottom (x − 2)(x − 3) from a math book. What is the top, multiplied out and combined?

   -x + 6
9. 9.

   Zee simplifies the complex fraction (1 + 2/x)/(1 − 4/x²) on a worksheet. Which is its simplest form?

   • x/(x − 2)
   • (x − 2)/x
   • (1 + 2x)/(-3)
10. 10.

    Ari simplifies the complex fraction (1 − 3/x)/(1 − 9/x²) in a notebook. Which is its simplest form?

    • (1 − 3x)/(-8)
    • (x + 3)/x
    • x/(x + 3)