144. Sometimes it is convenient to express a single fraction as a group of fractions. 145. We may often express a fraction in an equivalent form, partly integral and partly fractional. It is then called a Mixed Expression. Thus the quotient is 2x-1, and the remainder - 4. 146. If the numerator be of lower dimensions than the denominator, we may still perform the division, and express the result in a form which is partly integral and partly fractional. Here the division may be carried on to any number of terms in the quotient, and we can stop at any term we please by taking for our remainder the fraction whose numerator is the remainder last found, and whose denominator is the divisor. Thus, if we carried on the quotient to four terms, we should have 162.x9 1+ 3x2* 2x = =2x-6x3+18x5 – 54x7 + . The terms in the quotient may be fractional; thus if x2 is divided by 3-a3, the first four terms of the quotient are 1 a3 ασ + + ая 210, and the remainder is a12 x10 147. Miscellaneous examples in multiplication and division occur which can be dealt with by the preceding rules for the reduction of fractions. EXAMPLES XVI. b. Express each of the following fractions as a group of simple fractions in lowest terms: Perform the following divisions, giving the remainder after four terms in the quotient: |