Fractions Definition and 606 Threads

In my physics courses I have seen this kind of notation several times now: $$ \frac {A/B} {C}$$ For instance: or To me it doesn't seem intuitive and ## \frac A {BC}## would seem like a neater way of writing it. Therefore I wonder if there's any specific reason to why people write it...

I am reading Stephen Lovett's book, "Abstract Algebra: Structures and Applications" and am currently focused on Section 6.2: Rings of Fractions ... I need some help with the proof of Proposition 6.2.6 ... ... ... Proposition 6.2.6 and its proof read as follows: In the above proof by...

I am reading Stephen Lovett's book, "Abstract Algebra: Structures and Applications" and am currently focused on Section 6.2: Rings of Fractions ... I need some help with the proof of Proposition 6.2.6 ... ... ... Proposition 6.2.6 and its proof read as follows: In the above proof by Lovett...

I am reading Stephen Lovett's book, "Abstract Algebra: Structures and Applications" and am currently focused on Section 6.2: Rings of Fractions ... I need some help with some remarks following Definition 6.2.4 ... ... ... The remarks following Definition 6.2.4 reads as...

I am reading Stephen Lovett's book, "Abstract Algebra: Structures and Applications" and am currently focused on Section 6.2: Rings of Fractions ... I need some help with some remarks following Definition 6.2.4 ... ... ... The remarks following Definition 6.2.4 reads as follows: In the...

Homework Statement This is something I need to show in order to solve the question I've been asked. I need to show that ##\sqrt{\frac{N_A}{N_D} } + \sqrt{\frac{N_D}{N_A} } = \frac{N_A + N_B}{\sqrt{N_A N_B}}## I know these two sides are equal because wolfram alpha says they are, and also because...

Hi, I'm new. Please bear with me because I'm not familiar with the code of this forum. I don't know how to enter a mixed fraction correctly, so I'm just going to write it out. Here is the problem: Four and five-ninths minus 2/3 Can someone explain to me why the answer is three and...

partial fractions $$\int\frac{3x^2+x+12}{(x^2+5)(x-3)} =\frac{A}{(x^2+5)}+\frac{B}{(x-3)}$$ $$3x^2+x+12=A(x-3)+B(x^2+5)$$ x=3 then 27+3+12=14B 3=B x=0 then 12=-3A+15 1=A $$\int\frac{1}{(x^2+5)} \, dx +3\int\frac{1}{(x-3)}\, dx$$ $\displaystyle...

$\tiny{242t.8.5.9}$ $\textsf{expand the quotient by}$ $\textbf{ partial fractions}$ \begin{align*}\displaystyle y&=\int\frac{dx}{9-25x^2} &\tiny{(1)}\\ \end{align*} $\textit{expand and multiply every term by $(3+5x)(3-5x)$}$ \begin{align*}\displaystyle...

Before Joseph paints his house, he pours blue paint into 2 buckets of different sizes. He notices that the volume of the larger bucket is 3 times the volume of the smaller bucket. At the end of the day, Joseph estimates that the larger bucket is 3/4 full and the smaller bucket is 1/3 full/ He...

Hello, I've heard that MCNP outputs delayed neutron fractions (beta) and neutron generation times (Lambda). Any ideas as to where in the output file it writes these? I've coppied and pasted the Godiva reactor code and run it, but I can't seem to find it in there. Best Regards, -TP

Homework Statement and the solution (just to check my work) Homework Equations None specifically. There seems to be many ways to solve these problems, but the one used in class seemed to be partial fractions and Taylor series. The Attempt at a Solution The first step seems to be expanding...

$\tiny{206.8.5.49}$ $\textsf{Express the integrand as sum of partial fractions}$ \begin{align} && I_{49}&=\int\frac{30s+30}{(s^2+1)(s-1)^3}\, ds& &(1)& \\ &\textsf{expand}& \\ && &=\displaystyle 15\int\frac{1}{(s^2+1)}\, ds -15\int\frac{1}{(s-1)^2}\, ds +30\int\frac{1}{(s-1)^3}\, ds&...

I am working on a experiment that injects CO2 and H2 at a specified mass flux. The mass fraction of each is 0.5. Given the total mass flux of the combined species, how would I find the mass flux of each individual specie? I was thinking it would just be a simple halving since the mass fractions...

In a few exercises, I've needed to get the union or intersection of fractions or percentages. I'm not confident I fully understand. If I need the intersection of $A = 0.75$ and $ B = 0.5$, do I just take the larger number and subtract the smaller number? So the $ A \cap B$ would be $0.25$? And...

Homework Statement In 2011 the ATLAS experiment had a total integrated recorded luminosity of ##5.08fb^{-1}## at 7TeV, and in 2012 of ##21.3fb^{-1}## at 8TeV. Under these conditions Higgs bosons can be produced in several ways including gluon-gluon fusion and vector boson fusion, which have the...

Homework Statement A vessel contains a mixture of benzene and o-xylene. At 473K the pressure in the vessel is 1000 kPa (abs). Using the data provided below, and any others necessary, what are the mass fractions of benzene in the liquid and vapour? Assume the liquid phase is an idea liquid...

struggling to remember anything about partial fractions, can anybody help me with this? 6x-5 (x-4) (x²+3)

$\textbf{206.5.64 integral by partial fractions} \\ \displaystyle I_{64}= \int\frac{9x^3-6x+4}{x^3-x^2} \, dx \\ \text{expand} \\ \displaystyle \frac{9x^3-6x+4}{x^3-x^2} = \frac{9(x^3-x^2)+9x^2+6x+4}{x^3-x^2} = 9 + \frac{9x^2+6x+4}{x^2(x-1)} \\ \textbf{stuck!}$

Can someone please explain why the following equation is true: (7 \div 4) \div (1 \div 2) = 7 \div 4 \div 1 \times 2 As in, why does the division become multiplication when the parentheses are removed?Thanks

(k / 2k + 1) + (1 / (2k)(2k+2)) = ((k+1) / (2k+2)) I would like to simplify the left side to prove that these two statements are equal. I'm not sure how to do this. Surely I can't find a common denominator with such complex variables and such? What is a good approach?

For example, say I want to convert 1/7 to its representation as a repeating decimal? Is the fastest way just to do long division, or is there a faster way?

I have this integral: $$\int_{}^{} \frac{1}{\sqrt{x} - {x}^{\frac{1}{3}}} \,dx$$ So, I can set $u^6 = x$ then $6u^5 du = dx$. I can substitute that in and get: $$6 \int_{}^{} \frac {u^5}{u^3 - u^2} \,du$$ Then I can simplify to $$6 \int_{}^{} \frac {u^3}{u - 1} \,du$$ But I'm unsure how...

As there is a repeated root, the partial fraction decomposition we should use is: $\displaystyle \begin{align*} \frac{A}{x - 1} + \frac{B}{\left( x - 1 \right) ^2 } + \frac{C}{x - 2} &\equiv \frac{x^2}{\left( x - 1 \right) ^2\,\left( x - 2 \right) } \\ \frac{A\,\left( x - 1 \right) \left( x - 2...

http://imgur.com/RNsBBoO (image) Can someone elaborate as to how he factored this? The textbook provided nothing else about factoring algebraic expressions with fractions than this image.It avoided fractions in factoring like a plague I guess. I understand the 3rd step to put the (x + 1)^(3/4)...

There are certain explanations on how integers might have evolved, like for example "the wings of a bird to symbolize the number two, clover--leaves three, the legs of an animal four, the fingers on his own hand five."1 Seeing all these, and making experience short--abstract, can be said to have...

Hey so I'm new to my TI nspire cx, still getting the hang of it. I've been trying to figure out how to get my eigenvector values to be fractions instead of decimals when I calculate them on here. Also, when I find the polynomial roots I get back decimals instead of fractions. I would like to...

I'm reading Gelfand's algebra, and I encountered some wonky stuff that I can't figure out on my own (hence my need for the book in the first place) in problem 42 of the book. Here is an explicit statement of the problem. I thought parts a. and b. were easy, but when it came to part c., I just...

Differentiate the following two problems. 1. x divided by the square root of x squared+ 1 2. The square root of x + 2 divided by the square root of x - 1 Thank you.

In terms of the electromagnetic spectrum, are there wavelengths of light corresponding to fractions of nanometers, for example, 0.5 nm, with their own photon energies? Or are whole nanometers "nature's smallests units" when it comes to the various existing wavelengths of light?

Hello, I am enrolled in calculus 2. Just having started a section in our textbook about integration by partial fractions, I eagerly began trying to use this integration technique wherever I could. After messing around for multiple days, I ran into this problem: ∫ 1/(x^2+1)dx I immediately...

hi all thanks for any help ,Can You solve: I have the answer in my book but I don't know how the answer is reached please show steps to solve, i can solve 2 sum fractions but not sure where to start with 3 or more sums involved

Hey there, my question is: do i always have to compare the answer of the multiplied prime numbers by dividing the numerator and denominator with the given answers to see which one is correct. or is there a way to to always see the accurate answer without having to compare them. here is my way...

Homework Statement The question is stated at the top of the attached picture with a solution 20160303_095831.jpg The correct results of the coefficients are A=2, B=-5, C=1 I have tried this problem multiple times and am still getting ugly coefficients. I have no idea why. A fresh pair of eyes...

$$\frac{\frac{u}{v}-\frac{{v}^{2 }}{v+4}}{\frac{{u}^{2}}{v}+\frac{v}{{u}^{2}}} =\frac{uv+4u-{v}^{3 }}{{v}^{2}+4v} \cdot\frac{{u}^{2}v}{{u}^{4}+{v}^{2}} =\frac{u^3 v^2+4{u}^{3}v-{u}^{2}v^4} {{u}^{4 }v^2+4{u}^{4}v+v^4+4{v}^{3} } =$$ $$=\frac{u^3 v+4{u}^{3}-{u}^{2}v^3} {{u}^{4...

hey so if you are taking a floor function of a fraction >1, is there any way to predict anything about it's factorization? what about when the numerator is a factorial and the denominator is made up of factors that divide said factorial but to larger exponents then those that divide the...

Mark44 submitted a new PF Insights post Partial Fractions Decomposition Continue reading the Original PF Insights Post.

Prove $\dfrac{3^{371}+5}{5^{247}+3}>\dfrac{2^{371}+3}{3^{247}+2}$.

Homework Statement integrate (4x+3)/(x^2+4x+5)^2 Homework EquationsThe Attempt at a Solution I know to solve this problem you have to work with partial fractions, in the solution we were given they solve as followed 4x+3=A(x^2+4x+5)'+B I don't know why they take the derivative of x^2+4x+5...

I have a question where f(x) = 20-2x^2/(x-1)(x+2)^2 and have solved for constants A,B and C. A = 2 B = -4 C = -4 I have worked this out myself. Now I am told to compute the indefinite integral and I am getting this answer but apparently it is wrong and I don't understand how? My answer...

Homework Statement Fractions ##\frac{a}{b}## and ##\frac{c}{d}## are called neighbor fractions if their difference ##\frac{ad - bc}{bd}## has numerator ##\pm 1##, that is, ##ad - bc = \pm 1##. Prove that (a) in this case neither fraction can be simplified (that is, neither has any common...

Homework Statement [/B] 5,00 moles of graphite and 5,00 moles of oxygen gas are stored in a metal bottle. The temperature is raised until the graphite starts burning. The burning produces a mixture of CO and CO2 gases in the vessel. After the temperature had returned to it's original value...

Hi Thanks for the help

Homework Statement Homework Equations trigonometric identities The Attempt at a Solution I did a trig substitution of u=tan(θ/2) and from that I could substitute cos(θ) = 1-u2/1+u2 dθ = 2/(1+u2) du = 1/2 sec2(θ/2) dθ I simplified a bit and changed the bounds to get 2du/(5u2 + 1)(1 + u2)2...

I came across the following question on the BBC website; Convert 0.272727 to a fraction. It was a multiple choice question so I could test each possible answer by dividing the numerator by the denominator until I got the right one. But it made me wonder how I could have answered it had it not...

(Wish there was a solutions manual...). Please check my workings below Show $ \int \frac{dz}{{z}^{2} + z} = 0 $ by separating integrand into partial fractions and applying Cauchy's Integral theorem for multiply connected regions. For 2 paths (i) |z| = R > 1 (ii) A square with corners $ \pm 2...

Hello, I was just introduced to this concept and I have solved a few problems, but I haven't come across any with denominators to a raised power yet. ∫ 1 / [(x+7)(x^2+4)] dx I would appreciate any directed help. 1. from the initial state I have broken the fraction into two assuming that...

I'm interested in the following inequality (which may or may not be true) Theorem 1: ##( \sum_{i=1}^n \frac{a_i} {n}\ )( \sum_{i=1}^n \frac{1} {b_i}\ ) > \sum_{i=1}^n \frac{a_i} {b_i}\ ## Where ##n ≥ 2, a_1 < a_2 < ... < a_n## and ##b_1 < b_2 < ... < b_n##. My attempt at a proof: 1) When n =...

Because technically, the numerator is smaller than the denominator as −2<−1 I know it's an extremely stupid question. I mean I know that I can just multiply −1 to the numerator and the denominator and I'll get 2/1 which is greater than one. But what exactly is happening here? A number that...

I have been presenting some data and I was asked to present it "better". The figures have been fractions of a percent (e.g. 0.05%) and I would like to convey how small that is to a layman. I don't want to go to Parts Per Million and my first thought is to say 1/20th of 1% represents 0.05%...