Lesson Worksheet: Simplifying Algebraic Fractions Mathematics • 10th Grade

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

Q1:

Simplify the fraction 2𝑥+7𝑥−𝑥𝑥.

  • A2𝑥−7𝑥−1
  • B−2𝑥+7𝑥−1
  • C2𝑥−7𝑥+1
  • D2𝑥+7𝑥−1
  • E2𝑥+7𝑥+1

Q2:

Fully simplify the fraction 9𝑥−15𝑥+𝑥3𝑥.

  • A3𝑥+5𝑥+13
  • B3𝑥+5𝑥−13
  • C−3𝑥−5𝑥+13
  • D3𝑥−5𝑥−13
  • E3𝑥−5𝑥+13

Q3:

Fully simplify (𝑥+4)(𝑥+3)(𝑥+2)(𝑥+4).

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

Q4:

Fully simplify (𝑥−2)(𝑥−2)(𝑥+2).

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

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−4𝑥−4𝑥+4.

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

Q8:

Fully simplify 𝑥+5𝑥−24𝑥+15𝑥+56.

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

Q9:

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)

Q10:

We are given that 4𝑥−16𝑥−20𝑥2𝑥−16𝑥+30=𝑎𝑥(𝑥+𝑏)𝑥+𝑐, where 𝑎, 𝑏, and 𝑐 are integers. Work out the values of 𝑎, 𝑏, and 𝑐.

  • A𝑎=2, 𝑏=−1, 𝑐=−3
  • B𝑎=−2, 𝑏=−1, 𝑐=−3
  • C𝑎=2, 𝑏=1, 𝑐=3
  • D𝑎=2, 𝑏=1, 𝑐=−3
  • E𝑎=−2, 𝑏=1, 𝑐=−3

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