Worksheet: Factoring Algebraic Fractions

In this worksheet, we will practice factoring quadratic expressions and working with algebraic fractions containing linear, quadratic, or cubic expressions.

Q1:

Which of the following functions are equal?

  • A ๐‘› ( ๐‘ฅ ) = ๐‘ฅ + 8 ๐‘ฅ ๏Šง , ๐‘› ( ๐‘ฅ ) = ( ๐‘ฅ + 8 ) ( ๐‘ฅ + 2 1 ) ๐‘ฅ ( ๐‘ฅ + 2 1 ) ๏Šจ
  • B ๐‘› ( ๐‘ฅ ) = ๐‘ฅ + 8 ๐‘ฅ ๏Šง , ๐‘› ( ๐‘ฅ ) = ( ๐‘ฅ + 8 ) ๏€น ๐‘ฅ โˆ’ 2 1 ๏… ๐‘ฅ ( ๐‘ฅ โˆ’ 2 1 ) ๏Šจ ๏Šจ ๏Šจ
  • C ๐‘› ( ๐‘ฅ ) = ๐‘ฅ + 8 ๐‘ฅ ๏Šง , ๐‘› ( ๐‘ฅ ) = ( ๐‘ฅ + 8 ) ( ๐‘ฅ + 2 1 ) ๐‘ฅ ( ๐‘ฅ + 2 1 ) ๏Šจ ๏Šจ
  • D ๐‘› ( ๐‘ฅ ) = ๐‘ฅ + 8 ๐‘ฅ ๏Šง , ๐‘› ( ๐‘ฅ ) = ( ๐‘ฅ + 8 ) ๏€น ๐‘ฅ + 2 1 ๏… ๐‘ฅ ( ๐‘ฅ + 2 1 ) ๏Šจ ๏Šจ ๏Šจ
  • E ๐‘› ( ๐‘ฅ ) = ๐‘ฅ + 8 ๐‘ฅ ๏Šง , ๐‘› ( ๐‘ฅ ) = ( ๐‘ฅ + 8 ) ( ๐‘ฅ โˆ’ 2 1 ) ๐‘ฅ ( ๐‘ฅ โˆ’ 2 1 ) ๏Šจ

Q2:

Simplify the function ๐‘› ( ๐‘ฅ ) = ๐‘ฅ + 7 ๐‘ฅ 6 ๐‘ฅ + 2 5 ๐‘ฅ + 4 รท 6 ๐‘ฅ โˆ’ ๐‘ฅ 3 6 ๐‘ฅ โˆ’ 1 ๏Šจ ๏Šจ ๏Šจ ๏Šจ .

  • A ๐‘› ( ๐‘ฅ ) = ๐‘ฅ + 7 ๐‘ฅ โˆ’ 4
  • B ๐‘› ( ๐‘ฅ ) = ๐‘ฅ + 4 ๐‘ฅ + 7
  • C ๐‘› ( ๐‘ฅ ) = ๐‘ฅ โˆ’ 4 ๐‘ฅ + 7
  • D ๐‘› ( ๐‘ฅ ) = ๐‘ฅ + 7 ๐‘ฅ + 4
  • E ๐‘› ( ๐‘ฅ ) = ๐‘ฅ + 7 ๐‘ฅ ๐‘ฅ + 4 ๐‘ฅ ๏Šจ ๏Šจ

Q3:

Simplify the function ๐‘› ( ๐‘ฅ ) = 9 ๐‘ฅ + 7 2 ๐‘ฅ + 1 รท 9 ๐‘ฅ + 7 2 5 ๐‘ฅ + 5 .

  • A ๐‘› ( ๐‘ฅ ) = 8 1 5
  • B ๐‘› ( ๐‘ฅ ) = 1 5
  • C ๐‘› ( ๐‘ฅ ) = 5 8 1
  • D ๐‘› ( ๐‘ฅ ) = 5

Q4:

Simplify the function ๐‘› ( ๐‘ฅ ) = ๐‘ฅ + 4 ๐‘ฅ โˆ’ 1 2 ๐‘ฅ โˆ’ 3 6 รท 5 ๐‘ฅ โˆ’ 1 0 ๐‘ฅ โˆ’ 1 2 ๐‘ฅ + 3 6 ๏Šจ ๏Šจ ๏Šจ .

  • A ๐‘› ( ๐‘ฅ ) = 5 ๐‘ฅ โˆ’ 6
  • B ๐‘› ( ๐‘ฅ ) = ๐‘ฅ + 6 5
  • C ๐‘› ( ๐‘ฅ ) = 5 ๐‘ฅ + 6
  • D ๐‘› ( ๐‘ฅ ) = ๐‘ฅ โˆ’ 6 5
  • E ๐‘› ( ๐‘ฅ ) = 1 5 ( ๐‘ฅ โˆ’ 6 )

Q5:

Which of the following functions are equal?

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q6:

Given that 8 ๐‘ฆ ๐‘ฆ + 2 ๐‘ฆ โˆ’ 9 ๐‘ฆ ๐‘ฆ + 2 ๐‘ฆ = โˆ’ 2 ๏Šจ ๏Šฉ ๏Šจ ๏Šจ , find the value of ๐‘ฆ .

  • A0
  • B 5 2
  • C4
  • D โˆ’ 3 2

Q7:

Simplify the function ๐‘› ( ๐‘ฅ ) = 5 ๐‘ฅ + 1 5 ๐‘ฅ + 5 รท 6 ๐‘ฅ + 1 8 4 ๐‘ฅ + 2 0 .

  • A ๐‘› ( ๐‘ฅ ) = 1 5 2
  • B ๐‘› ( ๐‘ฅ ) = 3 1 0
  • C ๐‘› ( ๐‘ฅ ) = 2 1 5
  • D ๐‘› ( ๐‘ฅ ) = 1 0 3
  • E ๐‘› ( ๐‘ฅ ) = 5 2 4

Q8:

Simplify the function ๐‘› ( ๐‘ฅ ) = ๐‘ฅ โˆ’ ๐‘ฅ โˆ’ 3 0 ๐‘ฅ โˆ’ 3 6 รท 5 ๐‘ฅ + 2 5 ๐‘ฅ + 1 2 ๐‘ฅ + 3 6 ๏Šจ ๏Šจ ๏Šจ .

  • A ๐‘› ( ๐‘ฅ ) = 5 ๐‘ฅ + 6
  • B ๐‘› ( ๐‘ฅ ) = ๐‘ฅ โˆ’ 6 5
  • C ๐‘› ( ๐‘ฅ ) = 5 ๐‘ฅ โˆ’ 6
  • D ๐‘› ( ๐‘ฅ ) = ๐‘ฅ + 6 5
  • E ๐‘› ( ๐‘ฅ ) = 1 5 ( ๐‘ฅ + 6 )

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