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Simplifying Algebraic Fractions by Factorising (1)

In this worksheet, students simplify algebraic fractions by factorising.

'Simplifying Algebraic Fractions by Factorising (1)' worksheet

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Simplify/Manipulate Algebraic Expressions/Fractions

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

Factorising expressions can sometimes be the key to further simplification of algebraic fractions.

In this worksheet, we will be using factors to simplify algebraic fractions.

 

Example

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

3x4 - 6x2
x2 - 2

 

Answer

 

Factorise the top to get

 

3x2 (x2- 2)
x2 - 2

 

Divide top and bottom by x2 - 2 to get

 

3x2 (x2- 2)
x2 - 2

 

Simplify to get the answer

3x2

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

3x2 - 5x
3x - 5

 

x

3x

3x - 5

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

9x2 - 15x
3x - 5

 

x

3x

3x - 5

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

6x2 + 9x
2x + 3

 

x

3x

3x - 5

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

2x2 - 9x
2x - 9

 

x

3x

3x - 5

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

25x2 - 15x
5x - 3

 

x

3x

5x

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

25x3 - 15x2
5x - 3

 

x

5x

5x²

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

18x3 - 18x2
3x - 3

 

6x²

6x

6x³

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

32x3 + 24x2
4x + 3

 

8x

8x²

8x³

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

32x4 + 24x3
4x + 3

 

8x

8x²

8x³

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

35x5 - 25x4
7x - 5

 

5x4

5x2

7x - 5

  • Question 1

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

3x2 - 5x
3x - 5

 

CORRECT ANSWER
x
EDDIE SAYS
x(3x - 5)
3x - 5
  • Question 2

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

9x2 - 15x
3x - 5

 

CORRECT ANSWER
3x
EDDIE SAYS
3x(3x - 5)
3x - 5
  • Question 3

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

6x2 + 9x
2x + 3

 

CORRECT ANSWER
3x
EDDIE SAYS
3x(2x + 3)
2x + 3
  • Question 4

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

2x2 - 9x
2x - 9

 

CORRECT ANSWER
x
EDDIE SAYS
x(2x - 9)
2x - 9
  • Question 5

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

25x2 - 15x
5x - 3

 

CORRECT ANSWER
5x
EDDIE SAYS
5x(5x - 3)
5x - 3
  • Question 6

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

25x3 - 15x2
5x - 3

 

CORRECT ANSWER
5x²
EDDIE SAYS
5x2(5x - 3)
5x - 3
  • Question 7

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

18x3 - 18x2
3x - 3

 

CORRECT ANSWER
6x²
EDDIE SAYS
6x2(3x - 3)
3x - 3
  • Question 8

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

32x3 + 24x2
4x + 3

 

CORRECT ANSWER
8x²
EDDIE SAYS
8x2(4x + 3)
4x + 3
  • Question 9

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

32x4 + 24x3
4x + 3

 

CORRECT ANSWER
8x³
EDDIE SAYS
8x3(4x + 3)
4x + 3
  • Question 10

Simplify the following algebraic fraction by first factorising the top or the bottom.

 

35x5 - 25x4
7x - 5

 

CORRECT ANSWER
5x4
EDDIE SAYS
5x4(7x - 5)
7x - 5
---- OR ----

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