CHAPTER IX

FRACTIONAL AND LITERAL EQUATIONS

FRACTIONAL EQUATIONS

163. Clearing of fractions. If an equation contains fractions, these may be removed by multiplying each term by the L. C. M. of the denominator.

Multiplying each term by 6 (Axiom 3, § 90),

2x-2(x-3)=72-3(x+4) — 6x.

Removing parentheses, 2x - 2 x + 6 = 72 − 3 x 12 - 6x.

Ex. 2. Solve

14

9

=

x-1 ̄x+1 x+3

Multiplying by (x − 1) (x + 1) (x+3),

5(x+1)(x+3)-14(x −1)(x + 3) = − 9 (x + 1) (x − 1).

9

1

33. (2x-9) +
( 9 ) + (x − 4 ) = 7 (3 x − 2) — (3 x − 5).

13

164. If two or more denominators are monomial, and the other polynomial, it is advisable first to remove the monomial denominators only, and after simplifying the resulting equation to clear of all denominators.

Ex. 1. Solve

16x3
10

=

2x-5 8x-1
5x-1

5

Multiplying each term by 10, the L. C. M. of the monomial denomina

165. Frequently it is advantageous to unite terms before the clearing of fractions.

or,

Ex. 2. Solve

x+1 x+4

x+2x+5

x+2 x+5 x+3 x+6

Uniting the fractions in each member separately,

x2+6x+5x2-6x-8 x2+8x + 12x2 - 8x - 15

(x+2)(x+5)

(x+3)(x+6)

Dividing both members by 3 and clearing fractions,

x2+9x+18= x2 + 7 x + 10.