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

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,

MARKS App · Accepted Answer

x + 1 x 2 / 3 - x 1 / 3 + 1 - x - 1 x - x 1 / 2 10 = x 1 / 3 + 1 - x 1 / 2 + 1 x 1 / 2 10 = x 1 / 3 - 1 x 1 / 2 10 Now the r + 1 t h Term T r + 1 = C r 10 x 1 / 3 10 - r · - 1 x 1 / 2 r For independent term 10 - r 3 - r 2 = 0 ⇒ r = 4 ⇒ T 5 = C 4 10 = 210

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