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 𝑥−4𝑥−4𝑥+4.

  • A𝑥+2𝑥−2
  • B𝑥−2𝑥−4
  • C𝑥+2𝑥−4
  • D𝑥+4𝑥+2
  • E𝑥−2𝑥+2

Q2:

Fully simplify (𝑥−2)(𝑥−2)(𝑥+2).

  • A𝑥−2𝑥+2
  • B𝑥+2𝑥−2
  • C𝑥+2𝑥
  • D𝑥𝑥−2
  • E1𝑥+2

Q3:

Fully simplify (𝑥−3)𝑥−6𝑥+9(𝑥−3).

Q4:

Fully simplify (𝑥+4)(𝑥+3)(𝑥+2)(𝑥+4).

  • A𝑥+2
  • B𝑥+3𝑥+2
  • C𝑥+4𝑥+2
  • D𝑥+3𝑥+4
  • E𝑥+2𝑥+3

Q5:

Fully simplify (𝑥−3)(𝑥−3)(𝑥+8).

  • A1𝑥−3
  • B𝑥−3(𝑥−3)(𝑥+8)
  • C1𝑥+8
  • D𝑥+3𝑥+8
  • E𝑥+3(𝑥−3)(𝑥+8)

Q6:

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

  • A𝑥+3
  • B𝑥−6
  • C𝑥−6𝑥−9𝑥−3
  • D𝑥−3
  • E1

Q7:

Fully simplify 𝑥(𝑥+3)(𝑥+2)(𝑥+3).

  • A𝑥+2𝑥
  • B𝑥+3𝑥+2
  • C𝑥𝑥+2
  • D1𝑥+2
  • E𝑥+2𝑥+3

Q8:

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

  • A𝑥+4𝑥+7
  • B𝑥+2𝑥+7
  • C𝑥+2𝑥+3
  • D(𝑥+4)(𝑥+2)(𝑥+7)
  • E(𝑥+4)(𝑥+2)(𝑥+7)

Q9:

Fully simplify 𝑥+5𝑥−24𝑥+15𝑥+56.

  • A𝑥+7𝑥−3
  • B𝑥+8𝑥+7
  • C𝑥+7𝑥+8
  • D𝑥−3𝑥+8
  • E𝑥−3𝑥+7

Q10:

Fully simplify 𝑥+3𝑥+2𝑥+4𝑥+3.

  • A1𝑥+3
  • B𝑥+1𝑥+3
  • C𝑥+3𝑥−2
  • D𝑥−2𝑥+3
  • E𝑥+2𝑥+3

Q11:

Given that 𝑥=3+√2 and 𝑦=3−√2, find the value of 𝑥𝑦−𝑥𝑥(𝑥+𝑦).

  • A343216
  • B49216
  • C29
  • D169
  • E1912

Q12:

Given that 10𝑐𝑥+48𝑐𝑥−2𝑐𝑥=𝑎𝑥+𝑏, find |𝑎|+𝑏.

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