180 ALGEBRA.
part of the work being performed by the rules explained in Chapter xiii.
200. There is one important point to be observed when an expression contains powers of a certain letter and also powers of its reciprocal. Thus in the expression 2.r + i + 4+.r^+^+7ar^-f|, or X af
the order of descending powers is
X X- x^
and the numerical quantity 4 stands between x and 1/x. The reason for this arrangement will appear in Chapter XXII.
Ex. Find the square root of 24 -r ^^ -^^^- §?!.
X' y y- X
Arrange the expression in descending powers of y.
->••- X ' y y- X y X- §J/_4 8^-8 + ? ^+24 X 32?/ X 8- _8£ + -, y y- g 8.r x^ y .'/-
Here the second term in the root, — 4, arises from division of '- — ^ by -^, and the third term, -, arises from division of 8 by — ^ ; XX y X ^y~y
