Rational Fraction Puns

https://imgur.com/a/UmlDUW8 Two things: the textbook keeps saying a-b = -(b-a) and I do not understand why those two are equal, but I roll with it.

Second: I have no idea where I went wrong in this problem

Hi!

I have 2 tasks about rational expression, that I really struggle with. Could someone help me? I know the answer, but I dont know how to get to it.

I can't post images here for any reason?

Here are three examples on how Horner's Method can be used to quickly calculate rational fractions with polynomials. The program code is presented for the HP 12C.

Horner's rule involves repeated factoring until the polynomial is represented as a multiplication of polynomials. The idea is to make it easier for some scientific calculators and four-function calculators to evaluate polynomials. Using Horner's Method for the generic cubic polynomial:

a * t^3 + b * t^2 + c * t + d

t * (a * t^2 + b * t + c) + d

t * (t * (a * t + b) + c ) + d

On an RPN keystroke calculator, such as the HP 12C a possible code would look like:

STO t (from the X stack)

RCL a

*

RCL b

+

RCL t

*

RCL c

+

RCL t

*

RCL d

+

RTN

Code here: http://edspi31415.blogspot.com/2020/05/hp12c-rational-fractions-and-horners.html

https://imgur.com/a/7Ome8P6

That last bit seems tricky.

Do you add, subtract and multiply rational numbers the Same as you would fractions ?

Hi all, I've been looking for intuitive geometric explanations for MFDs but haven't had much luck. Specifically, how can I visualise the transformation of these to partial fraction form. At eigenvalues of the "denominator" matrix polynomials, what happens in the punctured neighbourhood.

Sorry for the vague description, if that's the case. I'll be happy to elaborate if someone directs me to ask these questions in a better manner.

My background is mechanical engineering and I am familiar with control theory and can follow purely mathematical explanations upto a point :/

Looking forward to your inputs!

I have the following problem:

(2 / (m^2 - 3m + 2) ) + (2 / (m^2 - m - 2) )

fraction bar

( 2 / (m^2 - 1) ) + ( 2 / (m^2 + 4m + 3) )

Both the numerator and the denominator have different LCD's.

My question is: if I multiply these different LCD's to the numerator and denominator in order to attain a single numerator/denominator term (and later divide these), wouldn't this fundamentally and incorrectly change the fraction?

For example, it's not like I can multiply the fraction 2/3 with 2 * 5 / 3 *6 (different LCD's?) and still expect to fundamentally have the same fraction.

I'm having trouble swallowing this concept. Can anyone explain it better?

http://imgur.com/gallery/maf07BQ

Any help would be appreciated. Missed the notes for this so I'm lost and can't find anything online.

About a year ago in a summer math camp, I saw a problem posed that was something like the following:

You are standing at the origin of the typical Cartesian coordinate plane. At each lattice point, an tall but infinitesimally thin pillar is placed; assume that you are able to see pillars that are infinitely far away from you. As you look in a circle around you, what fraction of your vision is obstructed by these pillars?

The first step of the solution was to realize that if you looked either direction along a line y=mx, your vision would be obstructed iff m was rational - that would imply that m=p/q for some integers p and q, so the lattice point (q, p) would lie on this line and the corresponding pillar would thus obstruct your vision. The next (and much more challenging) step of the solution was to find precisely what fraction of the real numbers were rational, as this would also be the fraction of possible slopes for which your vision would be obstructed. I think that this is a very interesting question, but from here, I don't remember how the rest of the proof went or exactly what the answer was, and I haven't been able to find it online. Does anyone know any more about the solution to this problem?

((x^2 )/(x+2))-((a^2 )/(a+2))/(x-a)

Hey there, I have been trying to simplify this question from a precalc textbook I found at a thrift shop. I've probably tried at least 10 times to solve it. But I just can't figure out how to get the answer, and I don't know where I'm going wrong. There aren't any similar examples in the textbook so I'm lost. I have an idea that the solution involves the difference of squares but I don't understand how to implement that tool when the squares are in fractions like this. Anyways, I would appreciate any help with this question and even how to approach questions like this so I don't get stumped in the future?

I'm working on simplifying [(x^2 + 2 x - 8)/(8 x - 16)] / [(x^2 - 16)/(2 x + 10)]

Question 1) If we considered this expression to be a function, what would the domain of this be? The problem values I'm considering are 2, -4, 4, and -5.

8(2)-16=0 and 2(-5)+10=0 and (+or-4)^2 -16=0

In WolframAlpha, evaluting this expression for x=5 results in 0. I thought this would be undefined since you cannot have division by zero. I guess the question is, is something like 10/(10/0) equal to zero or undefined

Question 2) After simplifying the original expression you get (x+5) / (4x-16). It is my understanding that this is not equivalent to the original expression for all values of x so we must state excluded values along with our equivalence. What would this excluded values need to be? The original and the simplification both are undefined at 4, so does that need to be stated? Also, I'm still confused as to why 5 is an accepted value.

Thank you for your time. Hope my questions made sense. Sorry I'm not better with he reddit formatting

Hi all!

My Calculus I class is currently on Chapter 5 of Stewart’s “Single Variable Calculus” textbook. We took a quiz last week that had a very strange question on it...

Please evaluate the integral of [( 2+x^2 ) / ( 1+x^2 )] [proper notation]

Not a strange question at all if you know how to use partial fractions to integrate rational functions. Unfortunately we don’t get to Section 7.4 until the 2nd week of Calculus II…

I’m wondering if there’s any way to evaluate this integral without using that partial fractions technique, that maybe I missed.. I went back through my class notes, and through the textbook sections that we were quizzed on (4.9, 5.2, 5.5), and didn’t find anything remotely similar to the above problem.

Here's as far as I've gotten lol.

Any help would be much appreciated.

Thanks!

I was thinking that if you take a Maclaurin Series for a function such as x^(1/2) you could represent an irrational number such as 2^(1/2) as a series of fractions. If these fractions could be combined, wouldn't this make 2^(1/2) a rational number?

The problem: convert 5.2424242424 to a fraction. I got the answer using my calculator, but I need to show work..and I don't know how. Please help?!

Is 0 / 2 a rational number?