Grade 10 Maths · Algebra

Simplify an algebraic fraction

Simplify a fraction with letters by factorising the top and bottom and cancelling common factors (for example (x² − 4)/(x − 2) = x + 2).

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11) Multiply algebraic fractions grade 10 Part 1Kevinmathscience

11) Multiply algebraic fractions grade 10 Part 2Kevinmathscience

Simplication of algebraic fractions Grade 10 Maths: Multiplication and division of fractionsMiss Martins Maths and Science

Grade 10 Algebra Simplifying algebraic fractions: Exam QuestionsMiss Martins Maths and Science

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Question 1.3 · November 2024 · Paper 1 · National (DBE) · 3 marks

1.3 Consider the product

(1 + \frac{1}{2}) (1 + \frac{1}{3}) (1 + \frac{1}{4}) ... (1 + \frac{1}{n})

. Determine ALL the values of

n

(

n \geq 2

) for which the product will be an integer value.(3)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: simplify an algebraic fraction

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3. Question 3.1.1 · March 2025 · Provincial · 2 marks
Given: $f (x) = \frac{2 x + 3}{- x - 3}$
3.1 Given: $f (x) = \frac{2 x + 3}{- x - 3}$
3.1.1 Show that $f (x)$ can also be written as $f (x) = \frac{3}{x + 3} - 2$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Manipulate expression $f (x) = \frac{2 x + 3}{- ( x + 3 )} = \frac{- ( 2 x + 3 )}{x + 3}$
  $= \frac{- ( 2 x + 6 - 3 )}{x + 3} = \frac{- [ 2 ( x + 3 ) - 3 ]}{x + 3}$
  1 mark · Simplify an algebraic fraction
2. ✓
  Separate terms $= \frac{- 2 ( x + 3 )}{x + 3} + \frac{3}{x + 3} = - 2 + \frac{3}{x + 3}$
  1 mark · Simplify an algebraic fraction
4. Question 8.2.2 · May/June 2024 · Paper 1 · National (DBE) · 3 marks
8.2 Determine:
8.2.2 $g^{'} (x)$ if $g (x) = \frac{3 x ^{4} - 4 x ^{2} + 6}{x ^{2}}$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Divide by denominator to simplify $3 x^{2} - 4 + 6 x^{- 2}$
  1 mark · Simplify an algebraic fraction
2. ✓
  Derive polynomial terms $6 x$
  1 mark · Differentiate using the power rule
3. ✓
  Derive negative power term $- 12 x^{- 3}$
  1 mark · Differentiate using the power rule
5. Question 1.2.2 · November 2024 · Paper 1 · Provincial · 4 marks
1.2 Simplify the following expressions completely:
1.2.2 $\frac{x + 3}{x - 3} \times \frac{x ^{3} - 27}{x ^{2} - 9} \div \frac{x ^{2} + 3 x + 9}{x - 3}$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Change division to multiplication and invert $\frac{x + 3}{x - 3} \times \frac{x ^{3} - 27}{x ^{2} - 9} \times \frac{x - 3}{x ^{2} + 3 x + 9}$
  1 mark · Simplify an algebraic fraction
2. ✓
  Factorise numerators and denominators $\frac{x + 3}{x - 3} \times \frac{( x - 3 ) ( x ^{2} + 3 x + 9 )}{( x - 3 ) ( x + 3 )} \times \frac{x - 3}{x ^{2} + 3 x + 9}$
  2 marks · Simplify an algebraic fraction
3. ✓
  Cancel common factors to simplify $1$
  1 mark · Simplify an algebraic fraction
6. Question 2.3.2 · March 2022 · Provincial · 4 marks
2.3 Simplify the following expressions fully:
2.3.2 $\frac{y ^{2} - y - 2}{y ^{2} - 4} \times \frac{y ^{2} + 2 y}{y ^{2} + y}$ (4)
Show the memo (2 ticks)Memo
1. ✓
  Factorise numerators and denominators $\frac{( y - 2 ) ( y + 1 )}{( y - 2 ) ( y + 2 )} \times \frac{y ( y + 2 )}{y ( y + 1 )}$
  3 marks · Simplify an algebraic fraction
2. ✓
  Simplify $1$
  1 mark · Simplify an algebraic fraction

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