Page:Elementary algebra (1896).djvu/130

112 Rh (2) But if the numerator be not divisible by c, we have {}{}= {}{}

, by the preceding case.

142. Rule III. To multiply together two or more fractions. Multiply the numerators for a new numerator, and the denominators for a new denominator.

To find the value of : {}{}

Let x

Multiplying each side by b x d, we have

xxbxd= bxd = b d = Art. 37. = a c (Art. 140.] xbd = ac.

Dividing each side by bd, we have x = {}{}

Similarly, x2x2= {}{}; and so for any number of fractions.

143. Rule IV. To divide one fraction by another. Invert the divisor, and proceed as in multiplication. Since division is the inverse of multiplication, we may

define the quotient x, when A is divided by i to be such that