Expand the expression $$( \dfrac{x}{3}+\dfrac{1}{x})^5$$

Asked by Pragya Singh | 1 year ago |  74

##### Solution :-

$$( \dfrac{x}{3}+\dfrac{1}{x})^5$$

$$^5C_0(\dfrac{x}{3})^5+ ^5C_1(\dfrac{x}{3})^4\dfrac{1}{x}+ ^5C_2(\dfrac{x}{3})^3(\dfrac{1}{2})^2$$

$$+^5C_3(\dfrac{x}{3})^2(\dfrac{1}{x})^3+^5C_4(\dfrac{x}{3})(\dfrac{1}{x})^4+^5C_5(\dfrac{1}{x})^5$$

$$\dfrac{x^3}{243}+5(\dfrac{x^4}{81})(\dfrac{1}{x})+10(\dfrac{x^3}{27})(\dfrac{1}{x^2})$$

$$+10(\dfrac{x^2}{9})(\dfrac{1}{x^3})+5(\dfrac{x}{3})(\dfrac{1}{x^4})(\dfrac{1}{x^5})$$

$$\dfrac{x^3}{243}+\dfrac{5x^3}{81}+\dfrac{10x}{9x}+\dfrac{5}{3x^3}+\dfrac{1}{x^5}$$

Answered by Abhisek | 1 year ago

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