...polynomials. A rational fraction is proper if its numerator is of lower degree than its denominator ; improper if the degree of the numerator is equal to or greater than the degree of the denominator. Since an improper fraction can always be reduced to a polynomial plus...

...polynomials. A rational fraction is proper if its numerator is of lower degree than its denominator ; improper if the degree of the numerator is equal to or greater than the degree of the denominator. Since an improper fraction can always be reduced to a polynomial plus...

...integers, is integrated by resolving it into its partial functions by the ordinary rules of Algebra ; if the degree of the numerator is equal to or greater than the degree of the denominator, that is, if m = n or > n, the quotient must be first obtained by division....

...into partial fractions : 8-3x-a? , 3 ^- 11 a?+ 13* -4 ' ' " 3x-l 3a? — ' (2* -3) (2a?-7x + 6) 478. If the degree of the numerator is equal to, or greater than, that of the denominator, the preceding methods are inapplicable. Let it be required, for example, to separate — ^ — ^—...

...^log(3g-2 VO - 12a;). 28. CHAPTER II. INTEGRATION OF RATIONAL FRACTIONS. 8. Preliminary Operation. If the degree of the numerator is equal to, or greater than, that of the denominator, the fraction should be reduced to a mixed quantity, by dividing the numerator by the denominator. For...

...\f[j? + ~'x^±) ' 2хг-Пх+ 5 a3 - 2 ж2 + 3 x - 10 (ж - 3) (ж2 + 2 ж - 5) ж* + ж2 + 1 186. If the degree of the numerator is equal to or greater than that of the denominator, we may, by division, reduce the fraction to the sum of an integral expression, and a fraction whose...

...A rational fraction is proper if its numerator is of lower degree than its denominator ; imjinijier if the degree of the numerator is equal to or greater than the degree of the denominator. Since an improper fraction can always be reduced to a polynomial plus...

...18-5x-3я? 5 2-3ж-я;2-2яг1 x(x — 3)2 ' я?(x — I)2 О 3. 12ж2-11ж-38 (2x-3)(8x!-Wx-3) 378. If the degree of the numerator is equal to, or greater than, that of the denominator, the preceding methods are inapplicable. In such a case, we divide the numerator by the denominator...

...я? ~"" ' х(х + 12 ж2 - 11 ж- 38 . 3ж+13 (3ж-1)(2ж + 3)2 ' (2 ж — 3)(8ar| - 10 ж - 3) 378. If the degree of the numerator is equal to, or greater than, that of the denominator, the preceding methods are inapplicable. < In such a case, we divide the numerator by the denominator...

...be reduced to an integral or mixed expression by the operation of division, if the degree (§ 108) of the numerator is equal to, or greater than, that of the denominator. 1. Reduce - — - x~ to a mixed expression. о x 3 £_2=6^ 15*_ 2 =2 2 3x 3x 3x ¿x 3x 2. Eeduce -...