Worksheet: Simplifying Algebraic Fractions

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

Q1:

Fully simplify 𝑥4𝑥4𝑥+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 (𝑥2)(𝑥2)(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 (𝑥3)𝑥6𝑥+9(𝑥3).

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 25𝑥625 ft2 and each roll of sod has an area of 𝑥10𝑥+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 (𝑥3)(𝑥3)(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 𝑥6𝑥9𝑥3 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 (𝑥81) 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+5𝑥24𝑥+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: 15𝑥8𝑥7𝑥2𝑥+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

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