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After indicating the operation of multiplication strike out all the factors that are common to the numerator and denominator.

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Ax + 1

15.

Ans.

aRx(b + 2x) + a(x + b) — 1.

b(x - a)

CHAPTER

V.

I. EQUATIONS OF THE FIRST DEGREE.

Definitions.

70. An equation is an expression of equality between two quantities. Thus,

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is an equation, expressing the fact that æ is equal to the sum of 6 and c.

71. Every equation is composed of two parts, connected by the sign of equality. These parts are called members: the part on the left of the sign of equality, is called the first member; that on the right, the second member. Thus, in the equation,

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Either member of an equation may be 0; in this case the algebraic sum of the quantities in the other member is 0.

Classification.

72. Equations are divided into two classes : those containing but one unknown quantity, and those containing more than one unknown quantity. Each of these classes

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is subdivided into degrees. In the first class, the degree
is determined by the exponent of the highest power of
the unknown quantity, in any term; in the second class,
the degree is determined by the highest sum of the ex-
ponents of the unknown quantities, in any term.
Thus,

bx + cy = 0,

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are equations of the second degree;

az + bx? + cx = d, 23 + 2x2y + 3yx + 4y = 5, are equations of the third degree ;

ac" +pan-1 +92n-2 = 8, xn-2yê + axn-By+buyn-1 = d, are equations of the nth degree.

We shall first consider equations of the first degree, containing but one unknown quantity.

Definitions.

73. The transformation of an equation, is the operation of changing its form, without destroying the equality of its members.

74. The solution of an equation, is the operation of finding such a value for the unknown quantity, as will satisfy the equation; that is, such a value as, being substituted for the unknown quantity, will render the two members equal. This value is called a root of the equation.

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