Solution: Since a fraction indicates division, and the numerator is partly divisible by the denominator, we perform the division and obtain a quotient of x- 2 and a remainder of 3. ible by x + 1, we simply indicate the division and

As 3 is not divis

add the result to

1. Definitions and Principles.

141. Fractions having a common denominator are

similar.

142. Dissimilar fractions in their lowest terms must be reduced to higher terms to have a common denominator. This is done by mutiplying both terms by the same quantity [P. 56]. Therefore, the common denominator must contain each of the given denominators. Hence,

Prin. 60.-Any common multiple of the denominators of two or more fractions is a common denominator of the fractions.

Prin. 61.—The lowest common multiple of the denominators of two or more fractions in their lowest terms is. the lowest common denominator.

Note.-L. C. D. stands for lowest common denominator.

Solution The L. C. M. of the denominators is abc, which is, therefore, the L. C. D. [P. 61]:

Note. To determine the factor to be inserted in both terms of any fraction, divide the L. C. D. by the denominator of that fraction.

EXERCISE 62.

Reduce to similar fractions having the L. C. D.:

2

14.

1

5

2' (x − 2)2

− — − — and (1-2)

(x − 1) (2 − x)' (x − 2) (3 — x)'

3

(1 − x) (x − 3)

Prin. 62.—The sum of two or more similar fractions equals the sum of their numerators divided by their common denominator.

Prin. 63.—The difference of two similar fractions equals the difference of their numerators divided by their common denominator.

Note. Sometimes it is better not to combine all the fractions at one time.