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Welcome to GCSE Edexcel Maths revision.

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Topic M 18: Algebraic fractions.

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This video covers Higher tier.

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Factorise numerator and denominator before cancelling common factors. the fraction with numerator open bracket x squared minus 9 close bracket and denominator open bracket x plus 3 close bracket ,

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end fraction equals the fraction with numerator open bracket open bracket x minus 3 close bracket multiplied by open bracket x plus 3 close bracket close bracket and denominator open bracket x plus 3 close bracket ,

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end fraction equals x minus 3,

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for x is not equal to minus 3.

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Cancel factors,

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not individual terms in sums. the fraction with numerator open bracket x plus 3 close bracket and denominator open bracket x close bracket ,

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end fraction is 1 plus the fraction with numerator open bracket 3 close bracket and denominator open bracket x close bracket ,

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end fraction ,

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not 3.

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The denominator cannot be zero.

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Record restrictions from the original denominator even when its factors disappear after cancellation.

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A simplified expression does not restore excluded values.

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Worked example: the fraction with numerator open bracket 6 x squared close bracket and denominator open bracket 9 x close bracket ,

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end fraction equals the fraction with numerator open bracket 2 x close bracket and denominator open bracket 3 close bracket ,

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end fraction ,

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with x is not equal to 0.

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Divide coefficients by 3 and cancel a common factor x.

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To multiply,

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factorise and cancel across the complete numerator and denominator: the fraction with numerator open bracket x squared minus 4 close bracket and denominator open bracket x plus 1 close bracket ,

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end fraction multiplied by the fraction with numerator open bracket x plus 1 close bracket and denominator open bracket x minus 2 close bracket ,

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end fraction equals x plus 2,

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with x is not equal to minus 1 or 2.

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To divide, multiply by the reciprocal of the second fraction.

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Check that the divisor itself is not zero as well as checking all denominators.

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Worked example: the fraction with numerator open bracket x close bracket and denominator open bracket 3 close bracket ,

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end fraction divided by the fraction with numerator open bracket x squared close bracket and denominator open bracket 6 close bracket ,

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end fraction equals the fraction with numerator open bracket x close bracket and denominator open bracket 3 close bracket ,

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end fraction multiplied by the fraction with numerator open bracket 6 close bracket and denominator open bracket x squared close bracket ,

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end fraction equals the fraction with numerator open bracket 2 close bracket and denominator open bracket x close bracket ,

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end fraction ,

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where x is not equal to 0.

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For addition or subtraction,

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use a common denominator and combine whole numerators. the fraction with numerator open bracket 2 close bracket and denominator open bracket x close bracket ,

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end fraction plus the fraction with numerator open bracket 3 close bracket and denominator open bracket x plus 1 close bracket ,

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end fraction equals the fraction with numerator open bracket 2 multiplied by open bracket x plus 1 close bracket plus 3 x close bracket and denominator open bracket x multiplied by open bracket x plus 1 close bracket close bracket ,

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end fraction equals the fraction with numerator open bracket 5 x plus 2 close bracket and denominator open bracket x multiplied by open bracket x plus 1 close bracket close bracket ,

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end fraction .

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Worked example: the fraction with numerator open bracket 1 close bracket and denominator open bracket x minus 1 close bracket ,

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end fraction minus the fraction with numerator open bracket 1 close bracket and denominator open bracket x plus 1 close bracket ,

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end fraction equals the fraction with numerator open bracket open bracket x plus 1 close bracket minus open bracket x minus 1 close bracket close bracket and denominator open bracket open bracket x minus 1 close bracket multiplied by open bracket x plus 1 close bracket close bracket ,

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end fraction equals the fraction with numerator open bracket 2 close bracket and denominator open bracket x squared minus 1 close bracket ,

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end fraction ,

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with x is not equal to plus or minus 1.

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Bracket the subtracted numerator.

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Multiply both sides of an equation by a common denominator to remove fractions, while preserving the restrictions on x.

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Worked example: the fraction with numerator open bracket 2 close bracket and denominator open bracket x close bracket ,

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end fraction equals the fraction with numerator open bracket 3 close bracket and denominator open bracket x plus 1 close bracket ,

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end fraction gives 2 multiplied by open bracket x plus 1 close bracket equals 3 x,

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so x equals 2.

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This is allowed since x is neither 0 nor minus 1.

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Solutions obtained after clearing denominators must be checked in the original equation.

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Reject values that cause division by zero, even if they satisfy the rearranged polynomial.

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If a quadratic appears, solve it by factorisation or the quadratic formula and test every candidate against the domain.

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That completes Algebraic fractions.

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Revisit the notes and test yourself on the revision website.