CHAPTER XIV

FRACTIONAL AND LITERAL LINEAR EQUATIONS

PROBLEMS

173. To clear an equation of fractions is to change its form so that the fractions shall disappear. This change is accomplished by the use of the L. C. D. of the given fractions.

And the original equation is merely changed in form and is free from fractions.

In general, to clear an equation of fractions:

174. Multiply both members of the equation by the L. C. D. of the fractions, remembering that the sign of each fraction becomes the sign of its numerator. Solve the resulting integral equation. Illustrations:

Multiplying both members by the L. C. D., (x + 1)(x − 1),

(x − 1)2 - (x + 1)(x + 2) = 2 (x2 – 1) − 2 x2.

SPECIAL FORMS OF FRACTIONAL LINEAR EQUATIONS

(a) THE INDEPendent MonomiAL DENOMINATOR

The L. C. D. of the monomial denominators, 3, 2, and 6, is 6. Multiplying both members of the equation by 6, we have,

At this point note that all x-terms outside of the fraction disappear. In any simple equation of this type the unknown term similarly disappears when the equation is cleared of monomial denominators. If the unknown term does not disappear excepting from the fraction having the binomial denominator, error has been made in the work.