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What we desire to do in this section is to begin with rational expressions & ask what simpler rational expressions did we add and/or subtract to obtain the original expression. The procedure of doing it is called partial fractions & the result is frequently called the partial fraction decomposition.
The procedure can be a little long and on occasion messy; however it is really fairly simple. We will begin by trying to find out the partial fraction decomposition of,
P ( x )/ Q ( x )
Where both P(x) & Q(x) are polynomials & the degree of P(x) is smaller than the degree of Q(x). Partial fractions can just be done if the degree of the numerator is firmly less than the degree of the denominator. i.e. important to remember.
Hence, once we've determined which partial fractions can be performed we factor the denominator as wholly as possible. Then for each of the factor in the denominator we can utilize the following table to find out the term(s) we pick up in the partial fraction decomposition.
Notice that the first & third cases are actually special cases of the second & fourth cases respectively if we consider k = 1 . Also, it will entirely be possible to factor any polynomial down in product of linear factors ( ax+ b ) and quadratic factors ( ax2 + bx+ c ) some of which might be raised to a power.
If there is 1/4 of item X for every 7/12 of item Y, how much of item X is there for 7/10 of item Y?
the kinetic energy of an object varies directly as the square of its velocity. A certain object traveling at 80 feet per second has a kinetic enrgy of 240 foot-pounds. what would b
Perpendicular to y=3x-2 and through the point (6,4)
1. Construct a truth table for the following Boolean expressions: a) ABC + A'B'C' b) ABC + AB'C' + A'B'C' c) A (BC' + B'C) 2. Simplify the following expressions:
answer in scientific notation correct to the ten thousandths 471,598,000,000
Simpler method Let's begin by looking at the simpler method. This method will employ the following fact about exponential functions. If b x = b y then x
steps to figuring out the answer 3(2p-1)-5p=4
Example Find out all the zeroes of P ( x ) = x 4 - 7 x 3 + 17 x 2 -17 x + 6 . Solution We found the list of all possible rational zeroes in the earlier example. Follo
Determine a quadratic regression function that represents the distance the ball will travel in terms of its speed when it is hit at a 40 degree angle.
Solve 2 x 10 - x 5 - 4 = 0 . Solution We can reduce this to quadratic in form using the substitution, u = x 5 u 2 = x 10 By using this substitution the equa
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