The term independent of 'x' in the expansion of (x+1/(x^2/3 + x^1/3 + 1) - (x-1)/(x-x^1/2))^10 ​ Where x 0, 1 is equal to ​

Question

The term independent of 'x' in the expansion of \(\left(\frac{x+1}{x^{2/3}+x^{1/3} + 1} - \frac{x-1}{x-x^{1/2}}\right)^{10}\), Where x \(\neq\) 0, 1 is equal to ............ .

Answer 1

Correct answer 210

For independent term

\(\frac{10-r}{3} - \frac{r}{2} = 0\) \(\Rightarrow\) r = 4

\(\Rightarrow\) T₅ = \(^{10} C_4 = 210\)