By Euler L.

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**Additional info for An algebraic problem of finding four numbers, given the products of each of the numbers with the sum of the three others**

**Sample text**

7. + a lOa + 25. 9x 12x + 4. + x2 13. 16. x2 19. 2 x x 25. x 28. x 2 40. 43. 46. 49. 2 . + + + 5x - 6. + x - 2. 2. llx - 12. + 4x - 5. + 12x - 13. - 2x 2 + 2 - 5x + 2. - 2. 5x - 6. 6x2 8x 14x - 15. 2 9x 3x - 2. 2 24x + 7x - 6. 36x2 + Qx - 10. 34. 5x 2 37. -24rs+4s 3x 2 2 2 8. 3x 2 x2 17. 2 x 2 x 23. x 29. 32. 35. 38. 2 - + 1. + x 9. 4m2 2x + 6x 12. x 6. 15. x2 3x + 2. 18. x 2 21. x 2 24. x 2 2. llx - 12. 30. 2 2 36. + 13x + 5. +15x 27x -6x 2 2 + 3x - 6. 8. 2. - llx 4x 3. 7. 7. + 30. - 5. 2 2 39.

The sign before a fraction is or is not changed according as the number of factors whose signs are changed is odd or even. The altered factors may be all in the numerator or in the denominator, or they may be in both. 3. FRACTIONS 40 [Ch. Ill Example. ) l)(x - sXs - 3) = - 2) (3 -x) Here the minus sign is second step because the sign is 3, which is odd. RULE nators, the 4. add (x(x- l)(x l)(x - 2)(x 2)(x - _ 3) 3) inserted before the fraction in the number of factors there changed in To add or subtract fractions with the same denomior subtract the numerators and place the result over common denominator.

9 How many and how many prime factors, has each of terms, + the following expressions: (a) xyz; (b) x2 2. 37 In which of the two following cases missible: The numerator and denominator common term, (b) a common + x is 1; (c) z2 is ax have - 11 "' 13 - y)(x 15. 3(a? + y) a In these y (x ' - l)(x - 3(x . (x > x - + y) + x-y(x y)' - y (a + b)x - y)' (a + b)(x (x "' + + l)o +1 y)(x Explain the errors which have been made problems 14-17. 14 (a) x-y 1) + y) + 1 2(x + y) (x l)x + 1 x+l (x + l)a (x + 1) + 6' a + b + c 3(a; + y)(a + b + c) - y)(x + y) (x ax + ay (x + x + ?