Worksheet: Operations with Algebraic Fractions

In this worksheet, we will practice adding, subtracting, multiplying, and dividing algebraic fractions.

Q1:

Simplify 4 ๐‘ฅ โˆ’ 2 2 ๐‘ฅ โˆ’ 1 โˆ’ 3 ๐‘ฅ + 8 2 ๐‘ฅ โˆ’ 1 2 2 .

  • A ๐‘ฅ โˆ’ 1 0 ( 2 ๐‘ฅ โˆ’ 1 ) 2 2
  • B 7 ๐‘ฅ + 6 2 ๐‘ฅ โˆ’ 1 2
  • C 7 ๐‘ฅ + 6 ( 2 ๐‘ฅ โˆ’ 1 ) 2 2
  • D ๐‘ฅ โˆ’ 1 0 2 ๐‘ฅ โˆ’ 1 2
  • E 7 ๐‘ฅ โˆ’ 1 0 2 ๐‘ฅ โˆ’ 1 2

Q2:

Simplify 5 ๐‘ฅ โˆ’ 7 ๐‘ฅ 3 ๐‘ฅ โˆ’ 2 รท 2 ๐‘ฅ โˆ’ 5 4 ๐‘ฅ โˆ’ 7 ๏Šจ . Write your answer in fully factored form.

  • A ๐‘ฅ ( 5 ๐‘ฅ + 3 ) ( ๐‘ฅ โˆ’ 7 ) ( 3 ๐‘ฅ โˆ’ 2 ) ( ๐‘ฅ โˆ’ 5 )
  • B ( ๐‘ฅ โˆ’ 7 ) ( 4 ๐‘ฅ โˆ’ 7 ) ( 3 ๐‘ฅ โˆ’ 2 ) ( ๐‘ฅ โˆ’ 5 )
  • C ( ๐‘ฅ โˆ’ 7 ) ( ๐‘ฅ + 3 ) ( 3 ๐‘ฅ โˆ’ 2 ) ( 2 ๐‘ฅ โˆ’ 7 )
  • D ๐‘ฅ ( 5 ๐‘ฅ โˆ’ 7 ) ( 4 ๐‘ฅ โˆ’ 7 ) ( 3 ๐‘ฅ โˆ’ 2 ) ( 2 ๐‘ฅ โˆ’ 5 )
  • E ๐‘ฅ ( 5 ๐‘ฅ โˆ’ 7 ) ( 2 ๐‘ฅ โˆ’ 5 ) ( 3 ๐‘ฅ โˆ’ 2 ) ( 4 ๐‘ฅ โˆ’ 7 )

Q3:

Given that ๐‘Ž ๐‘ and ๐‘ ๐‘‘ are algebraic fractions, write ๐‘Ž ๐‘ + ๐‘ ๐‘‘ in the form ๐‘ฅ ๐‘ฆ .

  • A ๐‘Ž ๐‘ ๐‘ ๐‘‘
  • B ๐‘Ž + ๐‘ ๐‘ ๐‘‘
  • C ๐‘Ž + ๐‘ ๐‘ + ๐‘‘
  • D ๐‘Ž ๐‘‘ + ๐‘ ๐‘ ๐‘ ๐‘‘

Q4:

Write as a single fraction in its simplest form.

  • A 4 + 2 ๐‘ฅ ( ๐‘ฅ + 1 ) ( 2 ๐‘ฅ + 3 )
  • B ( ๐‘ฅ + 2 ) ( ๐‘ฅ + 3 ) ( ๐‘ฅ + 1 ) ( 2 ๐‘ฅ + 3 )
  • C 8 ๐‘ฅ ( ๐‘ฅ + 1 ) ( 2 ๐‘ฅ + 3 )
  • D 2 ( ๐‘ฅ + 2 ) ( ๐‘ฅ + 3 ) ( ๐‘ฅ + 1 ) ( 2 ๐‘ฅ + 3 )
  • E 4 + 2 ๐‘ฅ ( 2 ๐‘ฅ + 3 )

Q5:

Simplify 7 ๐‘ฅ 3 ๐‘ฆ + 8 ๐‘ฅ 9 ๐‘ฆ .

  • A 5 ๐‘ฅ 4 ๐‘ฆ
  • B 5 ๐‘ฅ 9 ๐‘ฆ 2
  • C 3 1 ๐‘ฅ 9 ๐‘ฆ
  • D 2 9 ๐‘ฅ 9 ๐‘ฆ

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.