Worksheet: Adding and Subtracting Algebraic Fractions

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

Q1:

Simplify 4𝑥22𝑥13𝑥+82𝑥1.

  • A𝑥102𝑥1
  • B7𝑥+62𝑥1
  • C7𝑥102𝑥1
  • D𝑥10(2𝑥1)
  • E7𝑥+6(2𝑥1)

Q2:

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

  • A𝑎𝑐𝑏𝑑
  • B𝑎𝑑+𝑏𝑐𝑏𝑑
  • C𝑎+𝑐𝑏+𝑑
  • D𝑎+𝑐𝑏𝑑

Q3:

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

  • A(𝑥+2)(𝑥+3)(𝑥+1)(2𝑥+3)
  • B2(𝑥+2)(𝑥+3)(𝑥+1)(2𝑥+3)
  • C4+2𝑥(2𝑥+3)
  • D8𝑥(𝑥+1)(2𝑥+3)
  • E4+2𝑥(𝑥+1)(2𝑥+3)

Q4:

Simplify 7𝑥3𝑦+8𝑥9𝑦.

  • A31𝑥9𝑦
  • B5𝑥4𝑦
  • C5𝑥9𝑦
  • D29𝑥9𝑦

Q5:

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

  • A8(𝑥+2)(𝑥1)
  • B6𝑥(𝑥+2)(𝑥1)
  • C62𝑥+1
  • D6𝑥+6(𝑥+2)(𝑥1)
  • E2(𝑥1)

Q6:

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

  • A1𝑥
  • B23𝑥12𝑥
  • C712𝑥
  • D77𝑥
  • E2312𝑥

Q7:

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

  • A32
  • B0
  • C52
  • D4

Q8:

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

  • A22𝑥1𝑥
  • B2𝑥2𝑥
  • C22𝑥𝑥
  • D2𝑥+2𝑥
  • E2𝑥21𝑥

Q9:

Write 2(𝑥3)+7(𝑥3) as a single fraction in its simplest form.

  • A23+7𝑥(𝑥3)
  • B19+7𝑥𝑥3
  • C197𝑥(𝑥3)
  • D19+7𝑥(𝑥3)
  • E197𝑥𝑥3

Q10:

Write 3𝑥6+2𝑥+6 as a single fraction in its simplest form.

  • A3𝑥+6𝑥36
  • B5𝑥+6𝑥36
  • C5𝑥+6𝑥6
  • D2𝑥+6𝑥36
  • E5𝑥+6𝑥36

Q11:

Simplify 33𝑥66𝑥.

  • A3𝑥(3𝑥)(6𝑥)
  • B6𝑥(3𝑥)(6𝑥)
  • C3𝑥(3𝑥)(6𝑥)
  • D9𝑥(3𝑥)(6𝑥)
  • E6𝑥(3𝑥)(6𝑥)

Q12:

Simplify 23𝑥15𝑥.

  • A7𝑥15
  • B157𝑥
  • C1315𝑥
  • D15𝑥13
  • E715𝑥

Q13:

Simplify 2𝑥5+3𝑥4.

  • A26𝑥15
  • B20𝑥23
  • C5𝑥9
  • D23𝑥20
  • E15𝑥26

Q14:

Simplify 4𝑥+3+2𝑥2.

  • A62𝑥+1
  • B2(3𝑥+1)(𝑥3)(𝑥2)
  • C2(3𝑥1)(𝑥+3)(𝑥2)
  • D2(3𝑥+1)(𝑥+3)(𝑥2)
  • E2(3𝑥1)(𝑥3)(𝑥+2)

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