Скачать или смотреть Algebraic Fractions (Q22 IGCSE Paper 2HR 2018)

In this video, Lee Guffick walks students through one of the most challenging questions on the 2018 IGCSE Paper 2HR — simplifying algebraic fractions by factorising, expanding, cancelling and combining multiple elements into a single simplified expression.

This question is classic Grade 9 material and very similar to the early skills needed for A-Level Algebra. Lee breaks the problem into three manageable parts:

Factorising the numerator (difference of two squares),

Factorising the quadratic denominator using the rainbow/split-middle method,

Combining fractional expressions with algebraic denominators.

By the end, every factor cancels cleanly, leaving a beautifully simplified final answer — and students will understand why each step works.

⏱️ TIMESTAMPS:
00:00 – Introduction to the algebraic fractions question
00:14 – Recognising the numerator as a difference of squares
00:42 – Factorising 4x² − 25 into (2x − 5)(2x + 5)
01:10 – Using the rainbow split method to factorise the quadratic denominator
02:30 – Forming (5x + 7)(x − 1) from 5x² + 2x − 7
03:00 – Setting up the fractional expression to combine
03:40 – Using numerical analogy (⅓ − ¼) to explain algebraic subtraction
04:00 – Expanding the new numerator and collecting like terms
05:10 – Rewriting all three elements together
06:00 – Cancelling common factors across the entire expression
07:15 – Final simplified fraction

✏️ TOPICS COVERED:

Algebraic fractions

Difference of two squares

Factorising quadratics with the rainbow/split-middle method

Simplifying expressions with multiple algebraic denominators

Common factors and cancellation

Combining fractions into a single simplified expression

💯 EXAM TIPS:

If the question doesn’t mention exact values or decimals, it’s a strong clue that factorisation will be clean.

Check for obvious identities first: difference of two squares is extremely common in Grade 9 algebra.

Use the split-middle method when the coefficient of x² is not 1 — it keeps factorising systematic.

When combining algebraic fractions, think of the numerical equivalent (like ⅓ − ¼) to guide the structure.

After expanding, always check for cancellation before concluding your answer.

📚 ABOUT GUFFICK TUITION:
Lee Guffick is a former Head of Mathematics and A-Level Examiner helping students achieve A*/A grades and secure places at top universities including Oxford, Cambridge and the Ivy League. His algebra walkthroughs are known for clarity, structure and exam-driven technique that builds real confidence.

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