Expand (x-(1)/(x))^(1\\2) , simplifying the coefficients the right answer is x^(5)-5x^(3)+10x-(10)/(x) +(5)/(x^(3) )-(1)/(x^(5) ) but i can't work it out PLEASE HELP!

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asked Oct 9, 2022 132k views

2 votes

Expand
$(x-(1)/(x))^(1\\2)$ , simplifying the coefficients

the right answer is
x^(5)-5x^(3)+10x-(10)/(x) +(5)/(x^(3) )-(1)/(x^(5) )

but i can't work it out
PLEASE HELP!

Mathematics
high-school

Johannix asked

by Johannix

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1 Answer

3 votes

Answer:

Explanation:

In reality it is :
$(x-(1)/(x) )^5\\$

$Pascal'sTriangle\\\\\begin{array}{cccccc}1\\1&1\\1&2&1\\1&3&3&1\\1&4&6&4&1\\1&5&10&10&5&1\\\end{array}\\\\\\(x-(1)/(x) )^5\\\\=x^5+5*x^4*(1)/(x) *(-1)+10*x^3*(1)/(x^3)*(-1)+5*x*(1)/(x^4) +(1)/(x^5) *(-1)\\\\\\\boxed{(x-(1)/(x) )^5=x^5-5x^3+10x-(10)/(x) +(5)/(x^3) -(1)/(x^5) }$