III. To Reduce fractions in Algebra to their lowest terms, cancel out any factors common to numerator and denominator as in arithmetic; when the quantities readily split into factors, this can be done at sight; in more difficult cases find the G.C.M. of the numerator and denominator, and cancel this out of each, IV. To reduce algebraic fractions to one common denominator find the L.C.M. of the denominators, see how many times this will divide in each denominator, and multiply the number thus obtained into the numerator of that fraction: thus, reduce common denominators. x y d x e to V. To Add and Subtract fractions in Algebra, first bring them down to a common denominator, and then add or subtract the numerator as in arithmetic. Thus to take the example worked out in case 4, having reduced the fractions to the common denominator, the Answer=dex+ezy+day. If the problem had dey dex-ezy dey If the problem contain examples both of addition and subtraction, the same methods will be followed, as in the following Examples: 6 6 2ab 2ab a+ba-ba-b Here L.C.M. of a+b, a2-b2, and a-b-a2-b2. 2ab 2ab 6(a-b) 2ab 2ab(a+b) a+b+ a2b2-a-ba3_b2 + a2_b2 a2b2 6(a-b)+2ab―2ab (a+b) |