13.

1

14.

(x − a) (x − b)' (b − x) (c − x)' (x − c) (x − a)

1

(a - b) (a — c)' (b − c) (b − a)' (c − a) (c — b)

Reduce to one term:

x2+5 ax + 6 a2 x2 + 4 ax + 3 a2 x2 + 3 ax + 2 a2

166. Multiplication of Fractions.

how to multiply any two algebraical fractions.

+

We have now to show

Thus the product of any two algebraical fractions is another fraction whose numerator is the product of their numerators, and whose denominator is the product of their denominators.

The product of any number of fractions is found by the same rule.

Thus to divide by any fraction is the same as to multiply by its reciprocal. [See definition of reciprocal, Art. 168.]

168. When two quantities are such that their product

is 1, each is said to be the reciprocal of the other.

b

a

1

is the reciprocal of and is the reciprocal of a.

α

b

a

Thus

A quantity is small or large according as its reciprocal is large or small.

but

For example,

10000 <1000 <100 <10 <1,

10000 > 1000 > 100 > 10 >1.