139. If either numerator or denominator can readily be
resolved into factors we may use the following method.
Ex. Reduce to lowest terms {x^3-3x^2 -4x }{7 x3 - 18 x2 + 6 x + 5 }.
The numerator = x(x^2 + 3x — 4) = x(x + 4) (x — 1).
Of these factors the only one which can be a common divisor is the fraction = {x(x + 4)(x-1) } {7x2(x-1)-11x(x- 1)-5(x- 1) } ={x(x + 4) (x - 1)} {(x - 1) (7 x2 - 11 x - 5)} ={x(x + 4)} {7 x2 - 11 x - 6 }
EXAMPLES XIII. b.
Reduce to lowest terms :
J a^ - a^b - ah-^ -2b^ g 4 x^ + 3 ax^ + a^ a^ + 'Sa^b + S ab'^ + 2 6^ x^ + ax^ + ««x + a* 2 x3-5x2 4- 7x-3 jQ 4x3- 10x2 + 4x + 2 x3-3x + 2 " ' 3x4-2x3-3x + 2 ' 3 ft3 + 2 gg - 13 « + 10 jj 16x^-72x%^ + 81a^ a^ + a'^-10a--S ' ' 4x2 + 12 ax + 9 a^ ^ 2 x3 + 5 x^j/ - 30 X//2 + 27 ?/ ^g 6x3 + x2-5x-2 4x3 + 5x^/2-21 2/3 ■ ■ 6x3 + 5x2-3x-2' g 4 fl3 +12 a25 _ aj^-2 _ 15 jr^s ^^ Sx^ + 2x2 - 15x - 6 6a3 + 13a26_4a62- 15 63 ^ 7x3 - 4x2 - 21 x + 12 g 1 + 2 x2 + x3 + 2 x^ j^ 4x4 + 11x2 + 25 ■ - 1 + 3x2 + 2x3 + 3x4' ' 4x4- 9x2 + 30x-25" 7 x2-2x+l jg 3 x3 - 27 rtx2 + 78 a23; _ 72 ^a 3 x3 + 7 X - 10 2 x3 + 10 «x2 - 4 rt2x _ 48 a^ 3 a3 _ 3>a25 + ^^52 _ 53 ^^ ax3 - 5 a^x^ - 00 ff3a; + 40 gi 4 a2 - 5 «6 + 62 ' • a:* - 6 ax3 - 80 a-x'^ + 35 a^x
MULTIPLICATION AND DIVISION OF FRACTIONS.
140. Rule I. To multiply a fraction by an integer. Multiply the numerator by that integer; or, if the denominator be divisible by the integer, divide the denominator by it.
