\fdO'^ - Old Forge Coal Mines

(^) 2(1 + .t-)
2(1-^-)
ALGEBRA. 113
4(l + x), 4(1-A-), 2(l-.0
2, 2(1-^), 1-x
1, 1, 1
Hence, L. C. M. = 2(1 + x) x 2(1 - x) = 4(1 - x'). Ans.
(r) a-d (^a-d) {b-c), {b-c) {c-a), {c-a) {a-b)
b-c
{1,-c), {b-c) {c-a), {c-a)
1, c—a, c—a
1, 1, 1
Hence, L. C. M. = {a — b) {b — c) {c — a). Ans.
(21 6) 3,r» - 3 +rt -«;!'• = (3 - a)x* - 3 + ^ =
(3 — a) {x" — 1). Regarding jr' — 1 as {x^Y — 1, we have, by
Art. 462, x'-\ = {x^ _ i = (^' _ i) {x' + i). ^» - i z=
(4.- - 1) (jr' + ;r + 1) ; x^-\-\ = {x-\- 1) (;.;'- ^r + 1). Art.
466.
Hence, the factors are
(jr» + ;r + 1) (^'" - ;r + 1) {x + 1) {x _ 1) (3 - a). Ans.
(216) Arranging the terms according to the decreasing
powers of x, and extracting the square root, we have
x' + x^y + 4i^'y + ^xy^ + ^y' {x' + ^;r/ + 2y\ Ans.
2;^* + ^xy X y -\- 4.^xy»,.,»
2^' + ^J + 27' 4^y + 2-rj/' + 4j'
44r>» + 2ay/' + Ay'
(217) The arithmetic ratio of ^* — 1 to ;r + 1 is .r* — 1 —
{x-\-l) = x' - x-'l. Art. 381.
x' — \
The geometric ratio of -r* — 1 to ;r + 1 is —^tt- = x* -~ x*
-^x-l = {x* + l) {x - 1). Ans.
x^l