Algebraic fractions

A standard method from Number and algebra basics: the steps and worked examples.

Steps

Factorise every denominator.
Use the L.C.M. of the denominators as the common denominator.
Combine the numerators, keeping brackets around each one.
Expand, simplify, and cancel common factors.

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Worked examples

Example 1: Algebraic fractions: simplify 1/(x − 1) − 1/(x + 2).

= (x + 2)/[(x − 1)(x + 2)] − (x − 1)/[(x − 1)(x + 2)]
= [(x + 2) − (x − 1)] / [(x − 1)(x + 2)]
= 3 / [(x − 1)(x + 2)]

Example 2: Fractions: work out 2/3 + 3/4 and 5/6 ÷ 10/9.

2/3 + 3/4  = 8/12 + 9/12 = 17/12 = 1 5/12      L.C.M. of 3 and 4 is 12
5/6 ÷ 10/9 = 5/6 × 9/10                        multiply by the reciprocal
           = 45/60 = 3/4

For the whole topic, read Number and algebra basics: key points, common mistakes and how the DSE tests it.

Steps

Worked examples

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