\fdO'^ - Old Forge Coal Mines

ALGEBRA. 99
(6) So* -\- 2alf + 4(^' When adding polynomi-
5a* — Sad -\- b^ als, always place like terms
— *
tf + 5rt^ — b* under each other. (Art.
18a' - 20^^ - 19^' 393.)
14a' — ^^ab + I^V The coefficient of a* in
39a''-24a^+ 5^' Ans.
^^^ result will be 39, since
(+14) + (+18) + (-l) +
(+ 6) + (+ = 3) 39. When the coefficient of a term is not
written, 1 is always understood to be its coefficient. (Art.
359.) The coefficient of ab will be — 24, since (- 3) +
(-20) + (+ 5) + (- 8) + (+ 2) = - 24. The coefficient of b*
will be ( + 20) + (-19) + (-l) + (+l) + (+4) = +5.
Hence, the result or sum is 39a' — 24a^ + hb*.
{c) ^mn + 3a^ — ^c
+ Imn - ^ab + 3^ + 3w' — 4/
%mn — ab — 4:C
-{- 3x -{- dm^ — 4/ Ans.
(182) Thereciprocalof 3.1416is-—i—
=.3183+.
o.141d
Ans.
Reciprocal of . 7854 = = 1. 273 .
-=^ + Ans.
^r 1 1 64.32 .
.. „, „^ °f = ^ X = '^'^-
602 =-T- -T- ,t"\ . .„, .
(183) (a) —^ \-
^ ~ ^ . If the denominator of the
^ ' ^ ' X — y y — X
second fraction were written x — y^ instead oi y — x^ then
X — y would be the common denominator.
By Art. 482, the signs of the denominator and the sign
X 1/ X y
before the fraction may be changed, giving —.
We now have
_^c__x_-j!^x-x^y^_j^
X — y X — y X — y x — y
Ans.
X*
^
X
X -\-\
X
1 — X
(V) —5 --I r—7 — z . If we ^ write the ' denominator
x^ — \
of the third fraction x — 1 instead oil — x^ x"* — 1 will then
be the common denominator.