EXAMPLES FOR PRACTICE.

1. Divide a2+2ax+x2 by a+x.

• 2. Divide a3-3a2y+3ay2—y3 by a—y.

3. Divide 1 by 1-x.

4. Divide 6x4-96 by 3x-6.

Ans. a+x.

Ans. a2-2ay+y2.

Ans. 1+x+x2+x3, &c.

Ans. 2x3+4x2+8x+16,

5. Divide a55a4x+10a3x210a2x3+5ax-x5

by a2-2ax+x2.

Ans. a3-3a2x+3ax2-x3.

6. Divide 48x3-76ax264a2x+105a3 by 2x-3a. 7. Divide yo-3y4x2+3y2x1—x6 by y3—3y2x+3yx2

-x3.

ALGEBRAIC FRACTIONS.

PROBLEM I.

To reduce a mixed quantity to an improper fraction.

RULE.

Multiply the integer by the denominator of the fraction, and to the product add the numerator; and the denominator being placed under this sum, will give the improper fraction required.

-2x

a

8-7 to an improper fraction.

2x a

4. Reduce 1-- to an improper fraction. Ans.

To reduce an improper fraction to a whole or mixed

quantity.

RULE.

Divide the numerator by the denominator, for the integral part, and place the remainder, if any, over the denominator, and it will be the mixed quantity required.

PROBLEM III.

To reduce fractions of different denominators, to others of the same value, which shall have a common denominator.

RULE.

Multiply every numerator, separately, into all the denominators but its own, for the new numerators, and all the denominators together for the common denominator*.

and fractions required.

bed' bed' bcd'

* When the denominators have a common divisor, it will be better, instead of multiplying by the whole denominators, to multi. ply only by those parts which arise from dividing by the common divisor.

To find the greatest common measure of a fraction.

RULE*.

1. Range the quantities according to the dimensions of some letters, as is shown in division.

*The simple divisors, in this rule, may be easily found, by inspection.