please help me find the term independent of x in the expansion of (x + (3/x))^(−12 )


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Question Number 70310 by Rio Michael last updated on 03/Oct/19

$p l e a s e h e l p m e f i n d t h e t e r m i n d e p e n d e n t o f x$ $i n t h e e x p a n s i o n o f$ ${(x + \frac{3}{x})}^{- 12}$
Commented by mr W last updated on 03/Oct/19

$a l l t e r m s a r e x d e p e n d e n t!$
	Answered by MJS last updated on 03/Oct/19

	${(\frac{x^{2} + 3}{x})}^{- 12} = {(\frac{x}{x^{2} + 3})}^{12} \Rightarrow no term independent of x$
	Answered by mind is power last updated on 03/Oct/19

	${(x + \frac{3}{x})}^{12} ?$
	Commented by Kunal12588 last updated on 03/Oct/19

	$t h e n a n s w e r w o u l d b e 7 t h t e r m .$
	Commented by Rio Michael last updated on 03/Oct/19

	$t h a n k s g u y s$
	Commented by Rio Michael last updated on 03/Oct/19

	$n o, t o t h e - 12, i t c a m e o n a n o f f i c i a l e x a m i n a t i o n p a p e r$ $a n d i t r i e d a n d c o u l d n t s o l v e$
	Answered by MJS last updated on 03/Oct/19

	${(x + \frac{3}{x})}^{- 12} = {(\frac{x}{x^{2} + 3})}^{12} =$ $= \frac{1}{{(x^{2} + 3)}^{6}} - \frac{18}{{(x^{2} + 3)}^{7}} + \frac{135}{{(x^{2} + 3)}^{8}} - \frac{540}{{(x^{2} + 3)}^{9}} + \frac{1215}{{(x^{2} + 3)}^{10}} - \frac{1458}{{(x^{2} + 3)}^{11}} + \frac{729}{{(x^{2} + 3)}^{12}}$
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