Lesson Worksheet: Simplifying Algebraic Fractions Mathematics • 10th Grade

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

Q1:

Simplify the fraction 2๐‘ฅ+7๐‘ฅโˆ’๐‘ฅ๐‘ฅ๏Šซ๏Šฉ.

  • A2๐‘ฅโˆ’7๐‘ฅโˆ’1๏Šช๏Šจ
  • Bโˆ’2๐‘ฅ+7๐‘ฅโˆ’1๏Šช๏Šจ
  • C2๐‘ฅโˆ’7๐‘ฅ+1๏Šช๏Šจ
  • D2๐‘ฅ+7๐‘ฅโˆ’1๏Šช๏Šจ
  • E2๐‘ฅ+7๐‘ฅ+1๏Šช๏Šจ

Q2:

Fully simplify the fraction 9๐‘ฅโˆ’15๐‘ฅ+๐‘ฅ3๐‘ฅ๏Šฎ๏Šจ.

  • A3๐‘ฅ+5๐‘ฅ+13๏Šญ
  • B3๐‘ฅ+5๐‘ฅโˆ’13๏Šญ
  • Cโˆ’3๐‘ฅโˆ’5๐‘ฅ+13๏Šญ
  • D3๐‘ฅโˆ’5๐‘ฅโˆ’13๏Šญ
  • E3๐‘ฅโˆ’5๐‘ฅ+13๏Šญ

Q3:

Fully simplify (๐‘ฅ+4)(๐‘ฅ+3)(๐‘ฅ+2)(๐‘ฅ+4).

  • A๐‘ฅ+2
  • B๐‘ฅ+3๐‘ฅ+2
  • C๐‘ฅ+4๐‘ฅ+2
  • D๐‘ฅ+3๐‘ฅ+4
  • E๐‘ฅ+2๐‘ฅ+3

Q4:

Fully simplify (๐‘ฅโˆ’2)(๐‘ฅโˆ’2)(๐‘ฅ+2)๏Šจ.

  • A๐‘ฅโˆ’2๐‘ฅ+2
  • B๐‘ฅ+2๐‘ฅโˆ’2
  • C๐‘ฅ+2๐‘ฅ
  • D๐‘ฅ๐‘ฅโˆ’2
  • E1๐‘ฅ+2

Q5:

Fully simplify (๐‘ฅโˆ’3)(๐‘ฅโˆ’3)(๐‘ฅ+8)๏Šฉ๏Šฉ.

  • A1๐‘ฅโˆ’3
  • B๐‘ฅโˆ’3(๐‘ฅโˆ’3)(๐‘ฅ+8)
  • C1๐‘ฅ+8
  • D๐‘ฅ+3๐‘ฅ+8
  • E๐‘ฅ+3(๐‘ฅโˆ’3)(๐‘ฅ+8)

Q6:

Simplify ๐‘ฅโˆ’6๐‘ฅโˆ’9๐‘ฅโˆ’3๏Šจ as much as possible.

  • A๐‘ฅ+3
  • B๐‘ฅโˆ’6
  • C๐‘ฅโˆ’6๐‘ฅโˆ’9๐‘ฅโˆ’3๏Šจ
  • D๐‘ฅโˆ’3
  • E1

Q7:

Fully simplify ๐‘ฅโˆ’4๐‘ฅโˆ’4๐‘ฅ+4๏Šจ๏Šจ.

  • A๐‘ฅ+2๐‘ฅโˆ’2
  • B๐‘ฅโˆ’2๐‘ฅโˆ’4
  • C๐‘ฅ+2๐‘ฅโˆ’4
  • D๐‘ฅ+4๐‘ฅ+2
  • E๐‘ฅโˆ’2๐‘ฅ+2

Q8:

Fully simplify ๐‘ฅ+5๐‘ฅโˆ’24๐‘ฅ+15๐‘ฅ+56๏Šจ๏Šจ.

  • A๐‘ฅ+7๐‘ฅโˆ’3
  • B๐‘ฅ+8๐‘ฅ+7
  • C๐‘ฅ+7๐‘ฅ+8
  • D๐‘ฅโˆ’3๐‘ฅ+8
  • E๐‘ฅโˆ’3๐‘ฅ+7

Q9:

Fully simplify (๐‘ฅ+2)๏€น๐‘ฅ+7๐‘ฅ+12๏…(๐‘ฅ+7)(๐‘ฅ+10๐‘ฅ+21)๏Šจ๏Šจ.

  • A๐‘ฅ+4๐‘ฅ+7
  • B๐‘ฅ+2๐‘ฅ+7
  • C๐‘ฅ+2๐‘ฅ+3
  • D(๐‘ฅ+4)(๐‘ฅ+2)(๐‘ฅ+7)๏Šจ
  • E(๐‘ฅ+4)(๐‘ฅ+2)(๐‘ฅ+7)

Q10:

We are given that 4๐‘ฅโˆ’16๐‘ฅโˆ’20๐‘ฅ2๐‘ฅโˆ’16๐‘ฅ+30=๐‘Ž๐‘ฅ(๐‘ฅ+๐‘)๐‘ฅ+๐‘๏Šฉ๏Šจ๏Šจ, where ๐‘Ž, ๐‘, and ๐‘ are integers. Work out the values of ๐‘Ž, ๐‘, and ๐‘.

  • A๐‘Ž=2, ๐‘=โˆ’1, ๐‘=โˆ’3
  • B๐‘Ž=โˆ’2, ๐‘=โˆ’1, ๐‘=โˆ’3
  • C๐‘Ž=2, ๐‘=1, ๐‘=3
  • D๐‘Ž=2, ๐‘=1, ๐‘=โˆ’3
  • E๐‘Ž=โˆ’2, ๐‘=1, ๐‘=โˆ’3

Practice Means Progress

Download the Nagwa Practice app to access questions, unit-exams, and flashcards for your school courses.

scan me!

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