\fdO'^ - Old Forge Coal Mines

110 ALGEBRA.
(208) (a) Writing the work as follows, and canceling
common factors in both numerator and denominator (Arts,
496 and 497), we have
9 X 5 X 24 X vi^ifp'qx'y^ _ Smnxy .
8 X 2 X 90 X wz X « X /' X ^' X ;i^ X J 4/^'
(d) Factoring the numerators and denominators of the
fraction (Art. 498), and writing the factors of the numerators
over the factors of the denominators, we have
{a — x) (a' -f ax -{- x^) {a + •^) (^ + -^) _
{a + x) {a' — ax — — -\- x') [a x) {a x)
{a + x) {a'' -\-ax^ x') ^^^
{a — x) {a^ — ax -\- x^)'
(c) This problem may be written as follows, according to
Art. 480 :
Sax + 4 a^
a{'dax -j- 4) {Sax -f 4)"
Canceling a and (3«;r-|-4), we have- —— . Ans.
(209) (a) - Imy ) Zhm^y + 28;;?y - 14w/
— hm^ — 4;«y -f ^j'
Ans. (Art. 442.)
(d) a* W - ^a^b - a*b ) ^
4 — 'dab — d'b'' Ans.
{c) 4;r' ) 4,r' - S.r' + 12^' - 16;r'
X - 2x' + Sx' - Ax' Ans.-
(21 0) {a) IGa'b' ; a* + 4.ab ; 4^' - IGa'b + 5^* + 7ax.
(b) Since the terms are not alike, we can only indicate
the sum, connecting the terms by their proper signs.
(Art. 389.)
(c) Multiplication: 4«rV means 4 X ^ X ^' X ^. (Art.
358.)
^-^1 * )
^' 4- c' + ac a^-^c' — b' - 2ac
a'^b'-c'- 2ab ^
Arranging the terms, we have
a'c - ac*