The term independent of x in the expansion of (x+1x^2/3-x^1/3+1-x-1x-x^1/2)^10, where x0,1…

Question

The term independent of $x$ in the expansion of $\left(\dfrac{x+1}{x^{2/3}-x^{1/3}+1}-\dfrac{x-1}{x-x^{1/2}}ight)^{10}$, where $x
e0,1$ is equal to .......

Answer: 210

Accepted Answer

As shown in Question 31/135, this simplifies to $\left(x^{1/3}-x^{-1/2}\right)^{10}$, with independent term $r=4$:

$$T_5=\binom{10}{4}=210$$

Solutions · 1