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Asked by Phoebe-Lily

# How do you factorise/simplify algebraic fractions?

This type of problem depends on the example. At GCSE maths level, these problems require you to use maths tools such as Difference of Two Squares, Factorising Quadratics, adding and subtracting fractions. Some problems tell you to simplify an expression which has algebraic fractions. This has no equal sign, so your aim is to find an equivalent expression that is simpler than the original. In order to get to this, you should combine alrebraic fractions together using the common denominator method/cross multiply method when the fractions are being added/subtracted. After combining the fractions, work on the numerator and denominator separately. Expand any brackets, collect like terms and factorise the final quadratic. Do the same for the denominator. Sometimes you should use the difference of two squares rule; (A^2-B^2)=(A+B)(A-B) Then if the numerator and denominator have brackets in common, you can cancel them out. This should give you the answer in the simplest form. If the problem given has an equal sign, first follow the steps above. Then try and get the problem to be a line, rather than have fractions, by multiplying out the denominator to all terms of the equation. Then solve for the unknown.  Suhayl Patel
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