In this example, we see that x will divide both the numerator and denominator. Hence

In this example, the greatest measure of the numerator and denominator is obviously c+y. Hence,

(43.) To reduce a mixed quantity to the form of a fraction.

RULE.

Multiply the integral part by the denominator of the fraction, to which product add the numerator, and under the result place the given denominator.

EXAMPLES

x+y 7x

1. Reduce 11x+ to the form of a fraction.

In this example, the integral part is 11x, which, multiplied by the denominator 7x, gives 77x2, to which, adding the numerator x+y, we have 77x+x+y for the numerator of the fraction sought, under which, placing the denominator 7x, we finally obtain

Ans.

21a3-36-3a3y+6y—x2

4

7. Reduce a+b+b to the form of a fraction.

1-x

11. Reduce

1---x+x−1 to the form of a fraction.

CASE III.

(44.) To reduce a fraction to an integral, or mixed quantity.

RULE.

Divide the numerator by the denominator, the quotient will be the integral part; if there is a remainder, place it over the denominator for the fractional part.

We will now change the order of the terms of the numerator and denominator by placing the x2 first, we thus find this

SECOND OPERATION.

-6x+9a-8c1 | -x2+a

-6x2+6a

6=integral part.

3a-8c-numerator of fractional part.