Grade 10 Maths · Algebra

Clear fractions in an equation

Get rid of fractions in an equation by multiplying every term by the lowest common denominator (for example x/2 + x/3 = 5 becomes 3x + 2x = 30).

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Equations With Fractions Grade 9: IntroductionKevinmathscience

Equations With Fractions Grade 9: PracticeKevinmathscience

Grade 10 Equations with Fractions: Step by Step!Miss Martins Maths and Science

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Question 6.3 · November 2024 · Paper 1 · Provincial · 4 marks

The graphs of

f (x) = \frac{4}{x} - 2

and

g (x) = m x + c

are drawn below. A(4; 4), B, D(0; -4) and E are points on g. B is the x-intercept of both f and g. B and E are the points of intersection of f and g. AC is parallel to the y-axis, with C a point on f. Diagram for this question

6.3 Determine the coordinates of the point(s) of intersection of the two graphs algebraically.(4)

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

More past paper questions: clear fractions in an equation

Work each one out first, then open the memo and check every tick.

3. Question 3.1.2 · June 2024 · Paper 1 · Provincial · 4 marks
3.1 Solve for x:
3.1.2 $\frac{7}{3 - x} = \frac{5}{x + 3} + \frac{4}{x ^{2} - 9}$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Factorise denominators and adjust signs $\frac{- 7}{x - 3} = \frac{5}{x + 3} + \frac{4}{( x - 3 ) ( x + 3 )}$
  2 marks · Factorise a difference of squares
2. ✓
  Multiply by LCD and solve linear equation $- 7 (x + 3) = 5 (x - 3) + 4$
  $- 7 x - 21 = 5 x - 15 + 4$
  $- 12 x = 10$
  1 mark · Clear fractions in an equation
3. ✓
  Final answer $x = - \frac{10}{12}$
  $x = - \frac{5}{6}$
  1 mark · Clear fractions in an equation
4. Question 3.1.2 · March 2021 · Provincial · 2 marks
3.1 Simplify the following expression:
3.1.2 Hence, determine the value of x if: $\frac{x - 2}{3} - \frac{x + 4}{6} = 2$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute the answer from 3.1.1 $\frac{x - 8}{6} = 2$
  1 mark · Substitute into a formula
2. ✓
  Answer $x - 8 = 12 ⟹ x = 20$
  1 mark · Clear fractions in an equation
5. Question 2.1.2 · November 2024 · Paper 1 · Provincial · 4 marks
2.1 Solve for $x$ :
2.1.2 $\frac{2 x - 1}{3} \geq 2 x + 1$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Multiply by denominator $2 x - 1 \geq 3 (2 x + 1)$
  1 mark · Clear fractions in an equation
2. ✓
  Expand and simplify $2 x - 1 \geq 6 x + 3$
  1 mark · Multiply out a single bracket
3. ✓
  Group terms $- 4 x \geq 4$
  1 mark · Solve a linear inequality
4. ✓
  Solve for x (reversing inequality) $x \leq - 1$
  1 mark · Solve a linear inequality
6. Question 3.1.1 · March 2022 · Provincial · 4 marks
3.1 Solve for x in each of the following equations:
3.1.1 $\frac{3}{x + 2} + \frac{5}{x - 4} = 2$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Multiply by LCD $3 (x - 4) + 5 (x + 2) = 2 (x + 2) (x - 4)$
  1 mark · Clear fractions in an equation
2. ✓
  Expand and simplify $3 x - 12 + 5 x + 10 = 2 (x^{2} - 2 x - 8)$
  $8 x - 2 = 2 x^{2} - 4 x - 16$
  $2 x^{2} - 12 x - 14 = 0$
  1 mark · Write a quadratic in standard form
3. ✓
  Factorise $2 (x - 7) (x + 1) = 0$
  1 mark · Factorise a trinomial
4. ✓
  Solve $x = 7$ or $x = - 1$
  1 mark · Solve a quadratic by factorising

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