The coefficient of the term independent of x in the expansion o x+1x2/3−x1/3+1−x−1x−x1/210, is

We have ,x+1x2/3−x1/3+1−x−1x−x1/2=x1/33+13x2/3−x1/3+1−x−1x1/2x1/2−1=x1/3+1x2/3−x1/3+1x2/3−x1/3+1−x1/2+1x1/2=x1/3+1−1−x−1/2=x1/3−x−1/2∴ x+1x2/3−x1/3+1−x−1x−x1/210=x1/3−x−1/210Let Tr+1 be the general term in x1/3−x−1/210. Then,Tr+1=10Crx1/310−r(−1)rx−1/2rFor this term to be independent of x, we must have10−r3−r2=0⇒20−2r−3r=0⇒r=4S01 required coefficient =10C4(−1)4=210.