Grade 10 Maths · Algebra

Add or subtract algebraic fractions

Add or subtract fractions with letters by writing them over the lowest common denominator (for example 1/x + 1/2 = (2 + x)/(2x)).

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12) Add subtract fractions grade 10 | Part 2Kevinmathscience

12a) Add subtract fractions grade 10 | TryKevinmathscience

12b) Add subtract fractions grade 10 | TryKevinmathscience

Grade 10 and 11 Maths Algebraic Fractions How to Find the LCDMiss Martins Maths and Science

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Question 3.6 · June 2024 · Paper 2 · Provincial · 3 marks

3.6 Prove the identity:

\frac{1}{1 - c o s x} + \frac{1}{1 + c o s x} = \frac{2}{s i n ^{2} x}

(3)

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More past paper questions: add or subtract algebraic fractions

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3. Question 1.2.2 · March 2018 · Provincial · 3 marks
1.2 Simplify the following expressions fully:
1.2.2 $\frac{1}{m ^{3}} - \frac{1}{m ^{2}}$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Determine LCD $LCD = m^{3}$
  1 mark · Add or subtract algebraic fractions
2. ✓
  Combine fractions $\frac{1 - m}{m ^{3}}$
  2 marks · Add or subtract algebraic fractions
4. Question 1.2.2 · March 2015 · Provincial · 5 marks
1.2 Simplify the following expressions fully:
1.2.2 $\frac{1}{x ^{2} - 3 x - 4} + \frac{1}{4 - x}$ (5)
Show the memo (3 ticks)Memo
1. ✓
  Factorise denominator and adjust sign $\frac{1}{( x - 4 ) ( x + 1 )} - \frac{1}{x - 4}$
  2 marks · Add or subtract algebraic fractions
2. ✓
  Find LCD and combine $\frac{1 - 1 ( x + 1 )}{( x - 4 ) ( x + 1 )}$
  2 marks · Add or subtract algebraic fractions
3. ✓
  Simplify numerator $\frac{1 - x - 1}{( x - 4 ) ( x + 1 )} = \frac{- x}{( x - 4 ) ( x + 1 )}$
  1 mark · Collect like terms
5. Question 1.4.3 · March 2023 · Provincial · 5 marks
If $x \in {- 2; 2; 4; 5}$ , choose the value of $x$ from the given set that will make the expression $\frac{18}{4 - x}$ be:
1.4 Simplify the following expressions fully:
1.4.3 $\frac{x ^{2} - 4 x}{x ^{3} - 1} - \frac{1}{x - 1} - \frac{2}{x ^{2} + x + 1}$ (5)
Show the memo (4 ticks)Memo
1. ✓
  Factorise denominator $\frac{x ^{2} - 4 x}{( x - 1 ) ( x ^{2} + x + 1 )} - \frac{1}{x - 1} - \frac{2}{x ^{2} + x + 1}$
  1 mark · Factorise sum or difference of cubes
2. ✓
  LCD and numerator written out (double tick) $\frac{x ^{2} - 4 x - x ^{2} - x - 1 - 2 ( x - 1 )}{( x - 1 ) ( x ^{2} + x + 1 )}$
  2 marks · Add or subtract algebraic fractions
3. ✓
  Simplification of numerator $\frac{- 5 x - 1 - 2 x + 2}{( x - 1 ) ( x ^{2} + x + 1 )}$
  1 mark · Collect like terms
4. ✓
  Final Answer $\frac{1 - 7 x}{( x - 1 ) ( x ^{2} + x + 1 )}$
  1 mark · Collect like terms
6. Question 2.4 · March 2023 · Provincial · 5 marks
2.4 The product of two numbers x and y is 60 and their sum is 15. Show that $\frac{1}{x} + \frac{1}{y} = \frac{1}{4}$ (5)
Show the memo (5 ticks)Memo
1. ✓
  Equation 1 (product) $x y = 60$
  1 mark · Set up an expression or equation
2. ✓
  Equation 2 (sum) $x + y = 15$
  1 mark · Set up an expression or equation
3. ✓
  Adding the reciprocals $\frac{1}{x} + \frac{1}{y}$
  1 mark · Add or subtract algebraic fractions
4. ✓
  Finding the LCD $= \frac{y + x}{x y}$
  1 mark · Add or subtract algebraic fractions
5. ✓
  Substitute and Simplify $\frac{15}{60} = \frac{1}{4}$
  1 mark · Substitute into a formula

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