Mathematics - Binomial Theorem Question with Solution | TestHub

$\begin{array}{rl}& {\left(\frac{(x+1)}{\left(x^{\frac{2}{3}}+1-x^{\frac{1}{3}}\right)}-\frac{(x-1)}{\left(x-x^{\frac{1}{2}}\right)}\right)}^{10}\\ & ={\left(\left(x^{\frac{1}{3}}+1\right)-\left(\frac{\sqrt{x}+1}{\sqrt{x}}\right)\right)}^{10}\\ & ={\left(x^{\frac{1}{3}}-\frac{1}{\sqrt{x}}\right)}^{10}\\ & T_{r+1}={}^{10}{C}_r(x{)}^{\frac{10-r}{3}}(-1{)}^r(x{)}^{-\frac{r}{2}}\\ & \frac{10-r}{3}-\frac{r}{2}=0\\ & (20-2r)-3r=0\\ & r^{10}=4\\ & \Rightarrow {}^{10}{C}_4(-1{)}^4=210\end{array}$