The disadvantage of the method is that it becomes as difficult as the number of terms that the expression has in the numerator as well in the denominator because it is a rational expression
. Even more, the substitution into (8) gets more complicated if higher order derivatives are encountered, mainly because the first derivative of a rational expression
lies in terms of another rational expression
with a squared denominator and if in the nonlinear equation exist several different x powers, another rational expression
with even more terms is generated.
You said rational expressions
work just like fractions, except you don't know what the x is.
In this paper, we will use the moments based approach for obtaining closed form rational expressions
of MGF  to evaluate the performance in terms of the outage probability and the error rate for different multilevel modulation schemes.
Gustafson and Frisk (both: mathematics, Rock Valley College) have updated this edition substantially but still make sure the humanities majors can understand their coverage of real numbers and their basic properties, equations and inequalities, graphing, polynomials, factoring polynomials, proportion and rational expression
, systems of equations and inequalities, roots and radical expressions, quadratic equations and graphic quadratic equations.
Using many word problems and worked out examples, the authors cover basic concepts and properties; equations, inequalities, and problem solving; polynomials; rational expressions
; exponents and radicals; quadratic equations and inequalities; equations and inequalities in two variables; conic sections; functions; systems of equations; and exponential and logarithmic functions.
The key of the combination method is that the solutions are supposed as rational expressions
of elliptic functions of different moduli, which should be applicable to other nonlinear evolution equations or systems with bilinear forms in mathematical physics.
The power of RHPM method is based on the capability of rational expressions
containing a huge amount of information of dynamics from asymptotic problems.
We also give new explicit rational expressions
for [[mu].sub.n](a, b, c, d; q) so that [(abcd).sub.n][[mu].sub.n] (a, b, c, d; q) are clearly polynomials in a, b, c, d and q, see Theorem 4.2 and Theorem 4.3.
The chapters include a review of basic algebra, systems of equations, rational expressions
and equations, exponential and logarithmic functions, and conic sections with more graphing.
The stories of William Whiston and Elhanan Winchester describe Baptists who were drawn to rational expressions
This study used the experimental design with switching replication; that is, the two classes, designated here as Group 1 and Group 2, were alternately exposed to the blended learning strategy and the traditional face-to-face classroom instruction strategy in the delivery of selected topics in Algebra, namely, Algebraic Expressions, Special Products and Factoring, Rational Expressions
and Linear Equations and Inequalities in One Variable.
are, via the addition formulas, rational expressions
of cl(2[bar.[omega]]/n k)) = [[gamma].sub.k] + [[bar.[gamma]].sub.t]/2 and sl(2[bar.[omega]]/n k) = [[gamma].sub.k] - [[bar.[gamma]].sub.k]/2i.