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y = mx+b
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About this video
Simplifying algebraic fractions by factorising the top and the bottom first — and the cancelling rule behind it: only a whole bracket, or an identical top and bottom, may cancel.
What it covers
- The cancelling rule: the sign must be inside brackets
- Common factor, grouping, difference of squares and trinomials
- After cancelling, always check for more factorisation
- Products of fractions: factorise each part, then cancel
- Checking an answer by substituting your own number
Extra worked examples
✍️ Extra example: simplify (x² − 9)/(x² + 3x)
- 1((x − 3)(x + 3))/(x(x + 3))Difference of squares on top, common factor below.
- 2(x − 3)/xThe whole (x + 3) bracket cancels. The x's may NOT cancel — the top x is part of a bracket with a minus.
- 3Check with x = 1: (1 − 9)/(1 + 3) = −2 and (1 − 3)/1 = −2 ✓Give x your own number — the question and the answer must agree.
✍️ Extra example: simplify (x² + x − 6)/(3x + 9) × 6/(x − 2)
- 1((x + 3)(x − 2))/(3(x + 3)) × 6/(x − 2)Focus on one part at a time: the trinomial, then the common factor 3.
- 2(6(x + 3)(x − 2))/(3(x + 3)(x − 2)) = 2Write it as one fraction; both brackets cancel and 6 ÷ 3 = 2.
Exercises to try
Work each one out, then click to reveal the answer.
- 1Simplify (5x + 10)/5.
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(5(x + 2))/5 = x + 2 - 2Simplify (x² − 4x)/x.
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(x(x − 4))/x = x − 4 - 3Simplify (x² − 16)/(x + 4).
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((x − 4)(x + 4))/(x + 4) = x − 4 - 4Simplify (x² + 5x + 6)/(x² − 4).
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((x + 2)(x + 3))/((x − 2)(x + 2)) = (x + 3)/(x − 2) - 5Simplify (xy + 2x + 3y + 6)/(x + 3).
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Grouping: (x(y + 2) + 3(y + 2))/(x + 3) = ((y + 2)(x + 3))/(x + 3) = y + 2
