Page:Elementary algebra (1896).djvu/134

116 Rh The lowest common denominator is 6 ax(x — a)(x + a).

We must, therefore, multiply the numerators by 3 x(x + a) and 2 a respectively.

Hence the equivalent fractions are {16x2(x + a)} {6 ax(x — a) (x + a)} and {8a2 {6 ax(x — a){x + a)}

146. We may now enunciate the rule for the addition or subtraction of fractions.

Rule II. To add or subtract fractions. Reduce them to the lowest common denominator; add or subtract the numerators, and retain the common denominator.

Ex. 1. Find the value of {2x+a} {3a}+ {5x-4a}{ 9a }

The lowest common denominator is 9 a.

Therefore the expression = {3(2x + a)+ 5x - 4 a }{9a} _ n .r + .3 ft + 5 y — 4 g _ x — a {11x - a}{9a }

Ex. 2. Find the value of

The lowest common denominator is axy.

Thus the expression { a(x - 2 y) + x(3 y -a)- y(3x-2a) }{axy } ={ax — 2ay + 3xy — ax — 3xy + 2 ay } {axy }=0, since the terms in the numerator destroy each other.

EXAMPLES XIII. d.

Find the value of

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