43. RULE.-Reduce the fractions to a common denominator, subtract the numerator or the sum of the numerators of the fractions to be subtracted, from the numerator or the sum of the numerators of the others, and subscribe the common denominator.

44. When the denominators of the fractions which it is required to reduce are expressed in numbers, the result will frequently be much simplified by finding the least common multiple of the denominators, and then reducing the fractions to their least common denominator, according to the method explained in Arithmetic.

Thus, if we are required to reduce the following fractions:

a 3 x За 5 x
+

4

5

The least common multiple of 4 and 5 is 20, the denominator of the third fraction; therefore the fractions, when reduced to their least common denomi

the least common multiple of 3, 4, 6 is 12, which will be the least common denominator, and the above fractions become

12x+81-27 x — 10x—4—61+8x+20+ 29+ 4x— 5+37x

12

12

=2x+5

MULTIPLICATION OF FRACTIONS.

45. RULE.-Multiply all the numerators together for a new numerator, and all the denominators together for a new denominator. Thus,

(a + b) (e —ƒ) (k + 1) (p −q)

(3)xxx÷7=3=& (c+d) (g-h) (m −n) (r+ 8)

46. RULE.-Invert the divisor and proceed as in Multiplication.

47. Miscellaneous Examples in the operations performed in Algebraic Fractions

1

as

a b

3

3

1 -X

(12) 4(1°2)2 + 8(12=x) + 5(1+x) −4 (1+2°)

x)

2 X

9x+20

x2 + 3x + 2

b a a7b

=

(15)

2

x2+ x + 1

2

x2 + 5 x + 4

+7x+12

(ad + b c) fh
(eh+fg) ód

+

2

=

x2 - 11 x + 28

2

DIVISION OF FRACTIONS.

46. RULE.-Invert the divisor and proceed as in Multiplication.

47. Miscellaneous Examples in the operations performed in Algebraic Fractions