Worksheet: Adding and Subtracting Algebraic Fractions

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

Q1:

Simplify 4𝑥22𝑥13𝑥+82𝑥1.

  • A 𝑥 1 0 2 𝑥 1
  • B 7 𝑥 + 6 2 𝑥 1
  • C 7 𝑥 1 0 2 𝑥 1
  • D 𝑥 1 0 ( 2 𝑥 1 )
  • E 7 𝑥 + 6 ( 2 𝑥 1 )

Q2:

Given that 𝑎𝑏 and 𝑐𝑑 are algebraic fractions, write 𝑎𝑏+𝑐𝑑 in the form 𝑥𝑦.

  • A 𝑎 𝑐 𝑏 𝑑
  • B 𝑎 𝑑 + 𝑏 𝑐 𝑏 𝑑
  • C 𝑎 + 𝑐 𝑏 + 𝑑
  • D 𝑎 + 𝑐 𝑏 𝑑

Q3:

Write 4𝑥+1+2𝑥2𝑥+3 as a single fraction in its simplest form.

  • A ( 𝑥 + 2 ) ( 𝑥 + 3 ) ( 𝑥 + 1 ) ( 2 𝑥 + 3 )
  • B 2 ( 𝑥 + 2 ) ( 𝑥 + 3 ) ( 𝑥 + 1 ) ( 2 𝑥 + 3 )
  • C 4 + 2 𝑥 ( 2 𝑥 + 3 )
  • D 8 𝑥 ( 𝑥 + 1 ) ( 2 𝑥 + 3 )
  • E 4 + 2 𝑥 ( 𝑥 + 1 ) ( 2 𝑥 + 3 )

Q4:

Simplify 7𝑥3𝑦+8𝑥9𝑦.

  • A 3 1 𝑥 9 𝑦
  • B 5 𝑥 4 𝑦
  • C 5 𝑥 9 𝑦
  • D 2 9 𝑥 9 𝑦

Q5:

Write 4𝑥+2+2𝑥1 as a single fraction in its simplest form.

  • A 8 ( 𝑥 + 2 ) ( 𝑥 1 )
  • B 6 𝑥 ( 𝑥 + 2 ) ( 𝑥 1 )
  • C 6 2 𝑥 + 1
  • D 6 𝑥 + 6 ( 𝑥 + 2 ) ( 𝑥 1 )
  • E 2 ( 𝑥 1 )

Q6:

Write 23𝑥+54𝑥 as a single fraction in its simplest form.

  • A 1 𝑥
  • B 2 3 𝑥 1 2 𝑥
  • C 7 1 2 𝑥
  • D 7 7 𝑥
  • E 2 3 1 2 𝑥

Q7:

Given that 8𝑦𝑦+2𝑦9𝑦𝑦+2𝑦=2, find the value of 𝑦.

  • A 3 2
  • B0
  • C 5 2
  • D4

Q8:

Write 22𝑥 as a single fraction in its simplest form.

  • A 2 2 𝑥 1 𝑥
  • B 2 𝑥 2 𝑥
  • C 2 2 𝑥 𝑥
  • D 2 𝑥 + 2 𝑥
  • E 2 𝑥 2 1 𝑥

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