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Factorisation — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSFactorisation2 Marks
Question
Factorise by the grouping method $:a^2+\frac{1}{a^2}-2-3 a+\frac{3}{a}$
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Answer

$ a^2+\frac{1}{a^2}-2-3 a+\frac{3}{a}$
$ =\left(a-\frac{1}{a}\right)^2-3\left(a-\frac{1}{a}\right)$
$ =\left(a-\frac{1}{a}\right)\left[\left(a-\frac{1}{a}\right)-3\right]$
$ =\left(a-\frac{1}{a}\right)\left[a-\frac{1}{a}-3\right]$

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