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?

   • (x − 1)/((x − 5)(x + 5))
   • -5/((x − 5)(x + 5))
   • (2x + 5)/((x − 5)(x + 5))
   • 5/((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))
   • (x − 6)/((x − 3)(x + 3))
   • (3x − 2)/((x − 3)(x + 3))
   • (5x + 6)/((x − 3)(x + 3))
3. 3.

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

   • (-x + 6)/((x − 3)(x + 2))
   • (2x − 3)/((x − 3)(x + 2))
   • (5x + 6)/((x − 3)(x + 2))
   • (-x − 6)/((x − 3)(x + 2))
4. 4.

   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
5. 5.

   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
6. 6.

   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
7. 7.

   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
8. 8.

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

   • (x + 3)/x
   • x/(x + 3)
   • (1 − 3x)/(-8)
9. 9.

   Bo simplifies the complex fraction (1 + 5/x)/(1 − 25/x²) in pencil. Which is its simplest form?

   • x/(x − 5)
   • (x − 5)/x
   • (1 + 5x)/(-24)
10. 10.

    Esme simplifies the complex fraction (2 − 2/x)/(1 − 1/x²) from a math book. Which is its simplest form?

    • 2x/(x + 1)
    • (x + 1)/(2x)
    • 2/(x + 1)