Worksheet: Multiplying and Dividing Rational Expressions

In this worksheet, we will practice multiplying and dividing rational expressions.

Q1:

Simplify 5๐‘ฅโˆ’7๐‘ฅ3๐‘ฅโˆ’2รท2๐‘ฅโˆ’54๐‘ฅโˆ’7๏Šจ. Write your answer in fully factored form.

  • A(๐‘ฅโˆ’7)(4๐‘ฅโˆ’7)(3๐‘ฅโˆ’2)(๐‘ฅโˆ’5)
  • B๐‘ฅ(5๐‘ฅ+3)(๐‘ฅโˆ’7)(3๐‘ฅโˆ’2)(๐‘ฅโˆ’5)
  • C๐‘ฅ(5๐‘ฅโˆ’7)(2๐‘ฅโˆ’5)(3๐‘ฅโˆ’2)(4๐‘ฅโˆ’7)
  • D(๐‘ฅโˆ’7)(๐‘ฅ+3)(3๐‘ฅโˆ’2)(2๐‘ฅโˆ’7)
  • E๐‘ฅ(5๐‘ฅโˆ’7)(4๐‘ฅโˆ’7)(3๐‘ฅโˆ’2)(2๐‘ฅโˆ’5)

Q2:

Simplify ๐‘ฅ+2๐‘ฅ+3ร—2๐‘ฅ+6๐‘ฅ+1.

  • A2๐‘ฅ+1๐‘ฅ+4
  • B2๐‘ฅ+4๐‘ฅ+8
  • C3๐‘ฅ+4๐‘ฅ+1
  • D2๐‘ฅ+4๐‘ฅ+1
  • E2๐‘ฅ+3๐‘ฅ+1

Q3:

Simplify ๐‘ฅ+4๐‘ฅโˆ’1ร—๐‘ฅ+1๐‘ฅ+3๐‘ฅโˆ’4๏Šจ.

  • A๐‘ฅ+1(๐‘ฅ+1)๏Šจ
  • B๐‘ฅ+1(๐‘ฅ+4)๏Šจ
  • C๐‘ฅ+1(๐‘ฅโˆ’1)๏Šจ
  • D๐‘ฅโˆ’1(๐‘ฅโˆ’1)๏Šจ
  • E๐‘ฅโˆ’1(๐‘ฅ+1)๏Šจ

Q4:

Simplify 2412(๐‘›+5)รท๐‘›+3(๐‘›+5)(๐‘›+3).

Q5:

Simplify 2๐‘ฅ๐‘ฅ+3รท2๐‘ฅ5๐‘ฅ+15.

Q6:

Simplify ๐‘ฅโˆ’1๐‘ฆร—๐‘ฆ๐‘ฅโˆ’1๏Šจ๏Šฉ.

  • A๐‘ฆ๐‘ฅ+1๏Šจ
  • B๐‘ฆ๐‘ฅโˆ’1๏Šจ
  • C๐‘ฅ+1๐‘ฆ๏Šจ
  • D๐‘ฅ+1๐‘ฆ๏Šฉ
  • E๐‘ฅโˆ’1๐‘ฆ๏Šจ

Q7:

True or False: โˆ’๐‘ฅ๐‘ฅ+1รท๐‘ฅโˆ’1โˆ’๐‘ฅ=1.

  • ATrue
  • BFalse

Q8:

Simplify ๐‘Ž2รท๐‘Ž10๏Šจ๏Šช.

  • A2๐‘Ž๏Šซ
  • B๐‘Ž5๏Šจ
  • C20๐‘Ž๏Šฌ
  • D5๐‘Ž๏Šจ
  • E๐‘Ž20๏Šฌ

Q9:

Complete the following: ๐‘ฅ+๐‘ฆ2รท๐‘ฅ๐‘ฆ8=โ€ฆ๐‘ฅ๐‘ฆ.

  • A4๐‘ฅ+4๐‘ฆ
  • B2๐‘ฅ+2๐‘ฆ
  • C4๐‘ฅ+๐‘ฆ
  • D4
  • E8๐‘ฅ+8๐‘ฆ

Q10:

Simplify 2๐‘ฅ๐‘ฆ๐‘งร—๐‘ง๐‘ฆ๐‘ฅ6(๐‘ฅ+๐‘ฆ+๐‘ง)๏Šจ๏Šซ๏Šฎ๏Šจ๏Šซ๏Šฎ.

  • A๐‘ฅ๐‘ฆ๐‘ง5(๐‘ฅ+๐‘ฆ+๐‘ง)๏Šฌ๏Šฉ
  • B๐‘ฅ๐‘ฆ3๐‘ง(๐‘ฅ+๐‘ฆ+๐‘ง)๏Šฌ๏Šฌ
  • C๐‘ฅ3๐‘ง(๐‘ฅ+๐‘ฆ+๐‘ง)๏Šฌ๏Šฌ
  • D๐‘ฅ๐‘ง3(๐‘ฅ+๐‘ฆ+๐‘ง)๏Šฌ๏Šฉ
  • E13(๐‘ฅ+๐‘ฆ+๐‘ง)

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