...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...

...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...

...into 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...denominator of the given fraction and whose numerators are independent of я in case of fractions corresponding to factors of the first degree, and of the form...

...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...

...6„, as was stated. Ex. 1. Separate into partial fractions ^—^- - —t -- (x + 3) (x* - 4) Since the degree of the numerator is less than the degree of the denominator, we assume x» + ll* + 14= A ___ S_,_0_ (x + 3) (x2 - 4) x - 2 x + 2 x + 3' ( ! where A, B, and C are constants....

...For reasons which will presently appear, the methods to be explained apply only to fractions in which the degree of the numerator is less than the degree of the denominator. When this is not the case, divide numerator by denominator until a remainder of less degree than the...

...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...

...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...

...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...

...For reasons which will presently appear, the methods to be explained apply only to fractions in which the degree of the numerator is less than the degree of the denominator. When this is not the case, divide numerator by denominator until a remainder of less degree than the...