Question

factorise a/b+b/a+b/c+c/b+a/c+c/a+3​

Answer 1

How do I factorise the algebraic expression a/b+b/a+b/c+c/b+c/a+a/c+3?

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a/b+b/a+b/c+c/b+c/a+a/c+3

=(a^2+b^2) /ab+(b^2+c^2) /bc+(c^2+a^2) /ca+3

=(ca^2+cb^2+ab^2+ac^2+bc^2+ba^2+3abc) /abc

={a^2(c+b+a-a) +b^2(c+a+b-b) +c^2(a+b+c-c) +3abc}/abc

={(a+b+c) (a^2+b^2+c^2) -(a^3+b^3+c^3–3abc) }/abc

={(a+b+c) (a^2+b^2+c^2-a^2-b^2-c^2+ab+bc+ca) })/abc

={(a+b+c) (ab+bc+ca) }/abc

=(a+b+c) (1/c+1/a+1/b)

=(a+b+c) (1/a+1/b+1/c)…… read factorisation

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