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Question
Expand the expression: `(x/3 + 1/x)^5`
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Solution
By using Binomial Theorem, the expression `(x/3 + 1/x)^5` can be explained as
= `C_0 (x/3)^5 + ^5C_1 (x/3)^4 (1/x) + ^5C_2 (x/3)^3 (1/x)^2 + ^5C_3 (x/3)^2 (1/x)^3 + ^5C_4 (x/3) (1/x)^4 + ^5C_5 (1/x)^5`
= `(x^5)/243 + 5 (x^4/81) (1/x) + 10(x^3/27)(1/x^2) + 10 (x^2/9)(1/x^3) + 5(x/3)(1/x^4) + 1/x^5`
= `x^5/243 + (5x^2)/81 + 10/27 + 10/(9x) + 5/(5x^3) + 1/x^5`
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