Page:Elementary algebra (1896).djvu/58

40 Rh DIVISION OF A COMPOUND EXPRESSION BY A SIMPLE EXPRESSION.

57. Rule. To divide a compound expression hy a single factor, divide each term separately by that factor, and take the cdgehraic sum of the particd quotients so obtained. This follows at once from Art. 40.

Ex.1. (9x-12y + 3z) \div -3=-3x+4y -z. Ex. 2. (36 a^3b^2 - 24 a^2b^5 - 20 a^b^) - 4 a^b = 9 ab - 6b^4 - 5 a^2b. Ex. 3. (2 x^ - 5xy + x^^) - x = - ^x + y -xy^.

EXAMPLES V. a.

Divide

1. 3 x^3 by x^2. 15. - 50 y^x^ by - 5 x^y. 2. 27 x^ by - 9 x^ 16. x^-x^ + x by x. 3. - 35x^6 by 7 x^. 17. x^ - 1 x^ + 4x^4 by x^. 4. x^y^ by x^y. 18. x^ - 8x^6 + 3x^ by x^ 5. a^x^ by -a^x^. 19. 15x^5-25x^ by -5x^3. 6. 12a^6b^6c^6 by -3a^b^c^. 20. -24x^6-32x^ by -8x^3. 7. - a^5c^9 by - ac^3. 21. 34 x^y ^ - 51x^2^3 by xy. 8. 15x^y ^z ^ by 5x^2y^2z^2. 22. a^ - ab - ac by -a. 9. - 16 x^y^ by - 4 xy^. 23. a^3 - a ^b - a^2b^2 by a^. 10. - 48 a^9 by - 8 a^. 24. 3 x^3 - 9 x^y - 12 xy^ by - 3 x. 11. 63a^b^8c3 by 9a^5b^5c^3. 25. 4x^y^-8x^3y^2+6x^y^3 by -2xy. 12. 7 a^2bc by -7a^bc. 26. x^y^ - 3 x^3y^4 by - x^3y^2. 13. 28a^4b^3 by -4a^b. 27. - x^2+ xy + x by -  x. 14. 16 b^2^yx^2 by - 2 xy. 28. - 2 a^5x^3 + a^x^ by a^3x.

DIVISION OF COMPOUND EXPRESSIONS.

58. We employ the following rule:

Rule. 1. Arrange divisor and dividend according to ascending or descending powers of some common letter.

2. Divide the term on the left of the dividend by the term on the left of the divisor, and put the result in the quotient.