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" Q(x) to obtain a quotient (polynomial of the form g. ) plus a rational function (remainder divided by the divisor) in which the degree of the numerator is less than the degree of the denominator. "
Advanced Algebra - Page 140
by William Charles Brenke - 1917 - 196 pages
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Elements of the Differential and Integral Calculus with Applications, Volume 25

William Shaffer Hall - Calculus - 1897 - 282 pages
...dx, in which the last term is the only fractional term. So it is necessary to consider only rational fractions in which the degree of the numerator is less than the degree of the denominator. A rational fraction is integrated by decomposing it into a number of simpler partial fractions, which...
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A School Algebra Complete

Fletcher Durell, Edward Rutledge Robbins - Algebra - 1897 - 482 pages
...fractions by the use of the properties of identities. It is evident that if in the original fraction the degree of the numerator is less than the degree of the denominator, the same must be true in each partial or component fraction. The problem before us is the inverse of...
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College Algebra

James Harrington Boyd - Algebra - 1901 - 818 pages
...factors partly of tbe first arid partly of the second degree, or all of the second degree, in .r, and the degree of the numerator is less than the degree of the denominator, we can separate the given fraction by means of the theorem of undetermined coefficients into partial...
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College Algebra

James Harrington Boyd - Algebra - 1901 - 812 pages
...factors partly of the first and partly of the second degree, or all of the second degree, in x, and the degree of the numerator is less than the degree of the denominator, we can separate the given fraction by means of the theorem of undetermined coefficients into partial...
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An Algebra for High Schools and Academies

Louis Parker Jocelyn - Algebra - 1902 - 460 pages
...terminating, in the latter, non terminating. 240. A Proper Fraction in the literal notation is one in which the degree of the numerator is less than the degree of the denominator. ILLUSTRATIONS. 241. An Improper Fraction in the literal notation is a fraction in which the degree...
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A Text-book on Advanced Algebra and Trigonometry, with Tables

William Charles Brenke - Algebra - 1910 - 376 pages
...+ 4x2 - x3' 1 + 2x 1 17 79 x2 H 1 293 x» + ' 5з 2 6 36 216 1296 293 1 + 2x 1 i 17 , 7i .•A 236. Partial Fractions. — It is sometimes desirable to...can be factored into linear factors of the form (ax + b), no two factors being equal. The fraction can be resolved into a sum of simple fractions. of the...
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A Course in Mathematical Analysis, Volume 2

Edouard Goursat - Calculus - 1916 - 280 pages
...function, has a sense, provided that the denominator does not vanish for any real value of x and that the degree of the numerator is less than the degree of the denominator by at least two units. With the origin as center let us describe a circle C with a radius R large enough...
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A Course in Mathematical Analysis, Volume 2, Part 1

Edouard Goursat - Calculus - 1916 - 282 pages
...function, has a sense, provided that the denominator does not vanish for any real value of x and that the degree of the numerator is less than the degree of the denominator by at least two units. With the origin as center let us describe a circle C with a radius R large enough...
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A Course in Mathematical Analysis, Volume 2, Part 1

Edouard Goursat - Calculus - 1916 - 280 pages
...function, has a sense, provided that the denominator does not vanish for any real value of x and that the degree of the numerator is less than the degree of the denominator by at least two units. With the origin as center let us describe a circle C with a radius R large enough...
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Analytic Geometry and Calculus

Frederick Shenstone Woods, Frederick Harold Bailey - Calculus - 1917 - 536 pages
...(ax* + bx + e)""1 ax* + bx + c ' the above becomes a working rule for the integration of all rational fractions in which the degree of the numerator is less than the degree of the denominator; but the proof of the possibility of assuming the partial fractions in the form noted above is omitted....
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