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EXAMPLES WITH RADICAL SIGNS.

1.-Divide a3 + a√d + Nab + √63 by Na + vb.

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index of a

=

= a3, we find the index of the first term for the quotient, that is, from 3, 1 remains for the index of a in the quotient; the rest is evident from what has been before explained relative to indices.

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Ans...x+x3y + x2y2 + xy3 + y*.

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(ap)x2 + (ap + q)x aq by

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5

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5.-Divide (a2 - 4) (a2 — 4a) by a2 + 2a.

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6+2a 8 + a 10 by a

3+ a 5

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Ans...a

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·3+ a-5

It is evident that these negative powers, as well as positive, are divided by subtracting the indices; the Answers can be also written as follow:

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ALGEBRAIC FRACTIONS.

The operations in Arithmetic and Algebraic Fractions being nearly similar, it is judged unnecessary to say much on the subject.

To reduce a mixed quantity to an improper

fraction.

A mixed number is that which contains a whole number and a fraction, viz., 4 + is a mixed number, and, in reducing it to an improper fraction, we must find how many 8ths are in the whole number, thus, 32 + 5 4 x 8 + 5 = the improper fraction required.

8

RULE.

Multiply the whole number by the denominator of the fraction, and connect the numerator by the proper sign, placing the denominator under all.

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It will be here required to remember, that when a minus sign stands before a fraction with a compound numerator, each sign in that fraction must be changed.

To reduce an improper fraction to a whole or mixed number.

RULE.

Divide the numerator by the denominator, as in Arithmetic.

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Multiply each numerator into all the denominators except its own, for a new numerator of each fraction; and all the denominators into each other, for a new denominator, which will be common to each fraction.

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nator.

4x X b x 3 =

3 X b x 5 156 for a common denomiTherefore the new fractions will be,

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To find the greatest common measure of two
algebraical quantities.

RULE.

Divide the greater by the less, and divide the preceding divisor by the remainder, repeating the operation until nothing remains; the last divisor will be the common measure required.

1. Find the greatest common measure of a2 + a and a2 + 2a

a2 + a

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- 3.

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- 2

a

3(1
2

- 1)a2 + a
a2

− 2(a + 2

a

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