Edexcel IGCSE Maths (4MA1) · Unit 2: Algebra Basics
IGCSE Maths Algebraic Fractions Questions and Answers
Algebraic Fractions questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 3 worked examples first, then try the 3 exam-style questions yourself and check your working against the mark scheme.
Algebraic Fractions 3: Solving Equations: Solving equations with algebraic fractions, including ones that lead to quadratics.
Algebraic Fractions worked examples
Worked example 1: Simplifying an algebraic fraction
Simplify \(\dfrac{x^2-9}{x^2+5x+6}\).
Solution
Factorise the top: \((x-3)(x+3)\).
Factorise the bottom: \((x+2)(x+3)\).
Cancel \((x+3)\): \(\dfrac{x-3}{x+2}\).
Answer: \(\dfrac{x-3}{x+2}\)
Tip: Only cancel whole factors, never single terms.
Worked example 2: Adding algebraic fractions
Write \(\dfrac{2}{x}+\dfrac{3}{x+1}\) as a single fraction.
Solution
Common denominator \(x(x+1)\).
\(\dfrac{2(x+1)+3x}{x(x+1)}\).
\(=\dfrac{5x+2}{x(x+1)}\).
Answer: \(\dfrac{5x+2}{x(x+1)}\)
Tip: Multiply each numerator by the missing factor.
Worked example 3: Equation with algebraic fractions
Solve \(\dfrac{3}{x-1}-\dfrac{2}{x+1}=1\).
Solution
Multiply every term by \((x-1)(x+1)\): \(3(x+1)-2(x-1)=(x-1)(x+1)\).
\(x+5=x^2-1\), so \(x^2-x-6=0\).
\((x-3)(x+2)=0\), giving \(x=3\) or \(x=-2\).
Answer: \(x=3\) or \(x=-2\)
Tip: Check neither answer makes a denominator zero.
Algebraic Fractions exam-style questions
Try each question before you open the answer. The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.
Question 1 · easy · 3 marks
Solve \(\dfrac{x+4}{3} - \dfrac{x-2}{5} = 2\).
Show the answer and mark scheme
M1 multiplies all terms by 15 (or common denominator)
M1 5(x + 4) − 3(x − 2) = 30 with correct signs
A1 x = 2
Answer: \(x=2\)
Question 2 · medium · 3 marks
Solve \(\dfrac{5}{x+1} = \dfrac{3}{x-2}\).
Show the answer and mark scheme
M1 5(x − 2) = 3(x + 1)
M1 5x − 10 = 3x + 3 (collects terms)
A1 x = 6.5 oe
Answer: \(x=6.5\)
Question 3 · hard · 4 marks
Solve \(\dfrac{3}{x+2} + \dfrac{2}{x-1} = 1\). Give your solutions correct to 3 significant figures.
Show the answer and mark scheme
M1 3(x − 1) + 2(x + 2) = (x + 2)(x − 1)
M1 rearranges to x² − 4x − 3 = 0
M1 correct substitution into quadratic formula or completing the square, (x − 2)² = 7
A1 x = 4.65, x = −0.646 (accept 4.645…, −0.6457…)
Answer: \(x=4.65,\ x=-0.646\)
Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.
Which Edexcel IGCSE Maths papers test algebraic fractions?
Either Higher tier paper, 1H or 2H, can test algebraic fractions: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.
Where can I practise more algebraic fractions questions?
In the IGCSE student hub: Unit 2 (Algebra Basics) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.
IGCSE Math Revision