Simplify, multiply and divide rational expressions

Grade 11 Math Worksheet - Challenge Me

NameDate

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

  1. Jun multiplies (x² − 1)/(x² − 16) by (x − 4)/(x + 1) in a notebook. Which is the product in simplest form?

    • (x − 4)/(16(x + 1))
    • (x − 1)(x + 1)²/((x − 4)²(x + 4))
    • (x − 1)/(x + 4)
  2. Luz multiplies (x² − 36)/(x² − 1) by (x − 1)/(x − 6) from a math book. Which is the product in simplest form?

    • (x − 6)²(x + 6)/((x − 1)²(x + 1))
    • (x + 6)/(x + 1)
    • 36(x − 1)/(x − 6)
  3. Milo divides (x + 1)/(x² − 4) by (x + 5)/(x − 4) on a worksheet. What are all the excluded values of x?

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

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

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

  7. Tala rewrites (x + 3)/(x − 2) with the bottom x² − 4 on a worksheet. What is the new top, multiplied out?

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

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

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

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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. Jun multiplies (x² − 1)/(x² − 16) by (x − 4)/(x + 1) in a notebook. Which is the product in simplest form?

    • (x − 4)/(16(x + 1))
    • (x − 1)(x + 1)²/((x − 4)²(x + 4))
    • (x − 1)/(x + 4)
  2. Luz multiplies (x² − 36)/(x² − 1) by (x − 1)/(x − 6) from a math book. Which is the product in simplest form?

    • (x − 6)²(x + 6)/((x − 1)²(x + 1))
    • (x + 6)/(x + 1)
    • 36(x − 1)/(x − 6)
  3. 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
  4. 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
  5. Pia divides x/(x − 2) by (x + 4)/(x + 7) in pencil. What are all the excluded values of x?

    -7, -4, 2
  6. 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
  7. Tala rewrites (x + 3)/(x − 2) with the bottom x² − 4 on a worksheet. What is the new top, multiplied out?

    x² + 5x + 6
  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. Ari rewrites 5/(x + 1) with the bottom x² − 2x − 3 in pencil. What is the new top, multiplied out?

    5x − 15
  10. Bo rewrites 2x/(x − 5) with the bottom x² − 25 from a math book. What is the new top, multiplied out?

    2x² + 10x