of them may be found, by adding half the given difference to half the given sum; and the less, by subtracting half the given difference from half the given sum.” Ex. The sum of two numbers is 124, and their difference 18, what are the numbers? The rules for the management of Algebraic Fractions, are the same with those in common arithmetic; and, as these have been already explained, it would be superfluous again to detail the principles on which the various rules are founded. An example or two under each, will be sufficient to illustrate the various processes. 36. To reduce a fraction to its lowest terms. RULE. Find the greatest common measure of the terms of the fraction, as in Arithmetic, (No. 44.) and then divide them both by it. In finding the greatest common measure of two quantities, either of them may be multiplied or divided, by any number or quantity, Hence the greatest common measure of the two terms, is +b, and when they are both divided by it, we obtain x2 bx x+b for the given fraction in its lowest terms. The greatest common measure of the terms of a fraction, may often be found by mere inspection. 37. To reduce a whole number to an equivalent fraction, having any given denominator, (No. 45. Arith.) Ex. Reduce x + 2 to an equivalent fraction, whose denominator shall be y + 3. (x+2)(y+3)=xy+2y+3x+6, hence y+2y+3x+6 y+3 fraction sought. EXAMPLES. Ex. 1. Reduce a+b to an equivalent fraction, whose deno minator shall be a b. -- a2 62 Ans. a .b which is not a divisor of the other, or that contains no factor which is common to them both, without in any respect changing the result. In the present example, the remainder -2b x2 -2b2x is divided by ➡2bx, which gives the quotient x + b. |