The term independent of $\text{'}\mathrm{x}\text{'}$ in the expansion of  ${\left(\frac{\mathrm{x}+1}{{\mathrm{x}}^{2/3}-{\mathrm{x}}^{1/3}+1}-\frac{\mathrm{x}-1}{\mathrm{x}-{\mathrm{x}}^{1/2}}\right)}^{10}$ is P then $\left[\frac{\mathrm{P}}{25}\right]$  where [ . ] is G.I.F 

${\left(\frac{{\left(x^{1/3}\right)}^3+1^3}{x^{2/3}-x^{1/3}+1}-\frac{{\left(\sqrt{x}\right)}^2-1}{\sqrt{x}\left(\sqrt{x}-1\right)}\right)}^{10}$

$={\left(\left(x^{1/3}+1\right)-\frac{\sqrt{x}+1}{\sqrt{x}}\right)}^{10}$

$={\left(x^{1/3}-\frac{1}{x^{1/2}}\right)}^{10}$

Term independent of $\text{'}x\text{'}$  is  ${ }^{10}{C}_r$ . Where  $r=\frac{\frac{{\cancel{10}}^2}{\cancel{3}}}{\frac{\cancel{5}}{{\cancel{6}}_2}}=4$

${ }^{10}{C}_4=210$