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Suppose you have a fraction whose rational form is x/y where y is a positive integer. Furthermore, suppose that y = p*q where p and q are also positive integers (factors of y). Then x/y, in partial fraction form is: a/p + b/q for some integers a and b.
This may seem rather a tedious sort of exercise, but it comes into its own when analysing algebraic fractions, particularly for integration.
For example, suppose you need to find the integral of (3x + 2)/(x^2 + 3x + 2). A linear expression divided by a quadratic is not readily integrated. But
(3x + 2)/(x^2 + 3x + 2) = (3x + 2)/[(x + 1)*(x + 2)] which, in terms of partial fractions, is
-1/(x + 1) + 4/(x + 2)
Integrating, I[(3x + 2)/(x^2 + 3x + 2)] = I[-1/(x + 1) + 4/(x + 2)] = I[-1/(x + 1)] + i[4/(x + 2)]
= -ln(x + 1) + 4*ln(x + 2) + c where ln is the natural logarithm and c is a constant of integration
= ln[(x+2)^4 /(x+1)] + c
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What is a particle fraction?
i think you mean a partial fraction
In maths what is the fraction?
A fraction is part of a whole number as for example 1/4 is a quarter of 4
What do you get after multiplying each side of the partial fraction decomposition form by the least common denominator what do you get?
You get the original fraction.
What are the uses of fraction games for kids?
Fraction games are useful games for kids to learn about maths and numbers and provide an understanding of how fractions are part of everyday life. Games such as pizza games which show the amount of pizza left are all intended to aid children in understanding maths.
What does surd mean in maths?
A surd is an irrational number that can't be expressed as a fraction as for example the square root of 2
What is the partial amount in a fraction called?
It is the fraction. The non-partial part is called the integer part.
What is a particle fraction?
i think you mean a partial fraction
In maths what is the fraction?
A fraction is part of a whole number as for example 1/4 is a quarter of 4
Who nose how to do improper fraction can you learn me?
plesure help me with maths !
Does fraction cause heat?
Friction causes heat. Fraction causes heat only with people who are not comfortable with maths.
What do you get after multiplying each side of the partial fraction decomposition form by the least common denominator what do you get?
You get the original fraction.
A mixture of methane and helium is placed in a 2.0 l flask at 27 degrees the partial pressure of mathane is 0.72 ATM and the partial pressure of helium is 0.22 ATM What is the mole fraction of ch4?
To find the mole fraction of CH4, we first need to calculate the total pressure of the mixture. Total pressure = partial pressure of CH4 + partial pressure of He = 0.72 ATM + 0.22 ATM = 0.94 ATM. Then, we use the formula for mole fraction: Mole fraction of CH4 = (partial pressure of CH4) / (total pressure). Mole fraction of CH4 = 0.72 ATM / 0.94 ATM ≈ 0.766.
Why does integration by partial fractions work?
It is because the partial fractions are simply another way of expressing the same algebraic fraction.
What is a nice fraction?
I've always been partial to 2/3
What is partial assistance?
Someone who needs assistance for only a fraction of the time
Who is the father of fraction?
Sorry mate but I have no idea who it was, I think it was instine we all know he was a scientist but he also was an expert in maths , he used maths in his work and equations.
Who developed 4 partial differential equations that are one of the greatest achievements in maths in his ''treatise of electricity and magnetism?
James Clerk Maxwell
