Simplify, multiply and divide rational expressions

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Esme multiplies (x² − 4)/(x² − 9) by (x + 3)/(x − 2) on a worksheet. Which is the product in simplest form?

   • 4(x + 3)/(9(x − 2))
   • (x + 2)/(x − 3)
   • (x − 2)²(x + 2)/((x − 3)(x + 3)²)
2. 2.

   Kira multiplies (x² − 25)/(x² − 4) by (x + 2)/(x + 5) in pencil. Which is the product in simplest form?

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

   Luz multiplies (x² − 36)/(x² − 1) by (x − 1)/(x − 6) from a math book. Which is the product in simplest form?

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

   Milo divides (x + 1)/(x² − 4) by (x + 5)/(x − 4) on a worksheet. What are all the excluded values of x?

   -5, -2, 2, 4
5. 5.

   Noah divides (x − 3)/(x + 6) by (x − 1)/(x² − 9) in a notebook. What are all the excluded values of x?

   -6, -3, 1, 3
6. 6.

   Pia divides x/(x − 2) by (x + 4)/(x + 7) in pencil. What are all the excluded values of x?

   -7, -4, 2
7. 7.

   Ren divides (x + 2)/(x² − 5x + 6) by (x − 8)/(x + 1) from a math book. What are all the excluded values of x?

   -1, 2, 3, 8
8. 8.

   Zee rewrites (x − 1)/(x + 4) with the bottom x² + x − 12 in a notebook. What is the new top, multiplied out?

   x² − 4x + 3
9. 9.

   Ari rewrites 5/(x + 1) with the bottom x² − 2x − 3 in pencil. What is the new top, multiplied out?

   5x − 15
10. 10.

    Bo rewrites 2x/(x − 5) with the bottom x² − 25 from a math book. What is the new top, multiplied out?

    2x² + 10x