<s>[INST] $(\frac{x +1}{x^{2/3}-x^{1/3}+1} -\frac{x+1}{x-x^{1/2}})^{10}$ which term doesn't contain ${x}$? As I know  $T_{r+{1}}$=$C(n,r)$ 
I can't able to apply the formula for the Term which not contain $x$,which is applicable for this (${x +\frac{1}{x}})^n$
So, please help me to solve this problem . Any help will be appreciated 
 [/INST] Assuming the expression is 
$$\left(\frac{x +1}{x^{2/3}-x^{1/3}+1} -\frac{x-1}{x-x^{1/2}}\right)^{10}$$
The first term can be simplified setting $x^{1/3}=z\to x=z^3$
$\dfrac{x +1}{x^{2/3}-x^{1/3}+1}=\dfrac{z^3+1}{z^2-z+1}=z+1=x^{1/3}+1$
The second term simplifies in a similar way $x^{1/2}=z\to x=z^2$
$\dfrac{x-1}{x-x^{1/2}}=\dfrac{z^2-1}{z^2-z}=1+\dfrac{1}{x^{1/2}}$
The original expression simplifies to 
$$\left(x^{1/3}+1-1-\dfrac{1}{x^{1/2}}\right)^{10}=\left(\sqrt[3]{x}-\frac{1}{\sqrt{x}}\right)^{10}$$
Thus the terms non containing $x$ are those who simplify the cube and square roots, that is the $+a^6b^4$ term whose coefficient is $+\dbinom{10}{6}=210$
Hope this is useful
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