Page:Elementary algebra (1896).djvu/198

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