Ans. a1 .4 6a2b+6ab2 6a2+6a2b 2a3 ·2ab' 2a3. -2ab2 and 2a3- 2ab** ADDITION OF FRACTIONS. RULE. (26.) Reduce the fractions to a common denominator; and the sum of the numerators, written over the common denominator, will be the sum of the fractions. These fractions, reduced to a common denominator, become, respectively, 63x 30x 35.x and 105' 105 105' SUBTRACTION OF FRACTIONS. RULE. (27.) Reduce the fractions to a common denominator, and subtract one numerator from the other. and subtracting the numerator of the latter, gives for the dif 3bcxcx bc Subtracting, according to the rule, we have for the difference, ·bex + bx· - ab 2bcx + cx + bx — að bc CHAPTER II. EQUATIONS. (28.) An equation is the algebraic expression of equality between two quantities; x+12=4x-18, ax+ab—c—2a3 5x2 20 3 and +2x= +14 are equations. 3 The quantities on each side of the sign of equality are called members; that on the left is called the first member, and the other the second member. The quantities which compose a member are called terms, when they are connected together by the signs of addition and subtraction. Thus, in the equation ax + b = 3a — c + d, the first member has two terms, ax and b, and the second member three terms, 3a, c, and d. But in the equation (a-b) (2b+x) = 4a2, (a+b) (2b+x) is only one term; the quantities of which it is composed being connected by the sign of multiplication. In every equation there is supposed to be at least one unknown quantity expressed by a letter, and the solution of an equation consists in finding the value of this unknown quantity. An equation which has all its known quantities expressed by numbers, as 5x+4=11x-20 is called a numerical equation; one which has its known quantities expressed by letters, as ab-bx+ a2 = 3a3-3bx, is called a literal equation. Equations are of the first, second, third or fourth degree, according as the unknown quantity which they contain is of the first, second, third or fourth power. ax+b=3ax is an equation of the first degree, or simple equation. ax2 + bx=3ab is an equation of the second degree or quadratic equation. ax3 + bx2 + cx=2a1b is an equation of the third degree. ar1 + bx3+cx2 + dx=2ab3 is an equation of the fourth degree. |