Worksheet: Simplifying Algebraic Fractions

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In this worksheet, we will practice adding and simplifying algebraic fractions containing linear expressions with 2 or more variables.

Q1:

Fully simplify 𝑥−4𝑥−4𝑥+4.

  • A 𝑥 + 2 𝑥 − 2
  • B 𝑥 − 2 𝑥 − 4
  • C 𝑥 + 2 𝑥 − 4
  • D 𝑥 + 4 𝑥 + 2
  • E 𝑥 − 2 𝑥 + 2

Q2:

Fully simplify (𝑥−2)(𝑥−2)(𝑥+2).

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

Q3:

Fully simplify (𝑥−3)𝑥−6𝑥+9(𝑥−3).

Q4:

Fully simplify (𝑥+4)(𝑥+3)(𝑥+2)(𝑥+4).

  • A 𝑥 + 2
  • B 𝑥 + 3 𝑥 + 2
  • C 𝑥 + 4 𝑥 + 2
  • D 𝑥 + 3 𝑥 + 4
  • E 𝑥 + 2 𝑥 + 3

Q5:

Victoria wants to lay sod in her yard. The area of her yard is 25𝑥−625 ft2 and each roll of sod has an area of 𝑥−10𝑥+25 ft2. Find the number of rolls of sod she needs to buy. Write your answer as an algebraic fraction in its simplest form.

  • A 𝑥 + 5 2 5 ( 𝑥 − 5 )
  • B 𝑥 − 5 2 5 ( 𝑥 + 5 )
  • C 2 5 ( 𝑥 − 5 ) 𝑥 + 5
  • D 𝑥 − 1 2 5 𝑥 + 5
  • E 2 5 ( 𝑥 + 5 ) 𝑥 − 5

Q6:

Fully simplify (𝑥−3)(𝑥−3)(𝑥+8).

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

Q7:

Simplify 𝑥−6𝑥−9𝑥−3 as much as possible.

  • A 𝑥 + 3
  • B 𝑥 − 6
  • C 𝑥 − 6 𝑥 − 9 𝑥 − 3
  • D 𝑥 − 3
  • E1

Q8:

Fully simplify 𝑥(𝑥+3)(𝑥+2)(𝑥+3).

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

Q9:

George wants to mulch his garden. His garden is (𝑥+18𝑥+81) ft2 and one bag of mulch covers (𝑥−81) ft2. Write, in its simplest form, a rational function that describes the number of bags of mulch George needs to buy.

  • A 𝑥 + 9 𝑥 − 9
  • B 1 𝑥 + 9
  • C 𝑥 − 9 𝑥 + 9
  • D 1 𝑥 − 9
  • E 𝑥 + 9 𝑥 − 9

Q10:

Fully simplify (𝑥+2)𝑥+7𝑥+12(𝑥+7)(𝑥+10𝑥+21).

  • A 𝑥 + 4 𝑥 + 7
  • B 𝑥 + 2 𝑥 + 7
  • C 𝑥 + 2 𝑥 + 3
  • D ( 𝑥 + 4 ) ( 𝑥 + 2 ) ( 𝑥 + 7 )
  • E ( 𝑥 + 4 ) ( 𝑥 + 2 ) ( 𝑥 + 7 )

Q11:

Fully simplify 𝑥+5𝑥−24𝑥+15𝑥+56.

  • A 𝑥 + 7 𝑥 − 3
  • B 𝑥 + 8 𝑥 + 7
  • C 𝑥 + 7 𝑥 + 8
  • D 𝑥 − 3 𝑥 + 8
  • E 𝑥 − 3 𝑥 + 7

Q12:

Scarlett is tiling her bathroom floor. To find the number of tiles she needs, she writes the following rational expression, which divides the area of the room by the area of each tile: 15𝑥−8𝑥−7𝑥−2𝑥+1. Write this expression in its simplest form.

  • A 1 5 𝑥 − 7 𝑥 + 1
  • B 1 5 𝑥 + 7 𝑥 + 1
  • C 7 𝑥 − 1 5 𝑥 − 1
  • D 1 5 𝑥 − 7 𝑥 − 1
  • E 1 5 𝑥 + 7 𝑥 − 1

Q13:

Fully simplify 𝑥+3𝑥+2𝑥+4𝑥+3.

  • A 1 𝑥 + 3
  • B 𝑥 + 1 𝑥 + 3
  • C 𝑥 + 3 𝑥 − 2
  • D 𝑥 − 2 𝑥 + 3
  • E 𝑥 + 2 𝑥 + 3

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