This study notes covers Worked Example 2: Adding within Algebraic Fractions for GCSE Mathematics. Revise Algebraic Fractions in Algebra for GCSE Mathematics with 13 exam-style questions and 12 flashcards. This topic shows up very often in GCSE exams, so students should be able to explain it clearly, not just recognise the term. It is section 4 of 5 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Worked Example 2: Adding
Simplify: 3/x + 2/(x + 1)
Step 1 Find common denominator
Common denominator = x(x + 1)
Step 2 Adjust each fraction
= 3(x + 1)/[x(x + 1)] + 2x/[x(x + 1)]
Step 3 Combine and simplify
= [3(x + 1) + 2x]/[x(x + 1)]
= (3x + 3 + 2x)/[x(x + 1)]
= (5x + 3)/[x(x + 1)]
Practice questions for Algebraic Fractions
Simplify 6x²/3x
Explain why you need a common denominator when adding algebraic fractions.
Quick recall flashcards
Simplifying Algebraic Fractions
Factorise top and bottom FIRST, then cancel common factors
Graphical Inequalities
Solid line = ≤ or ≥. Dashed line = < or >. Shade region