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ChiralSuperfields
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- Homework Statement
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- Relevant Equations
- Please see below
How did they get y^7 in the bottom fraction? I got their answer except I had y^6. Would some please be able to help?
Many thanks!
Multiply both the top and bottom by ##y## to help simplify the numerator...Callumnc1 said:Homework Statement:: Please see below
Relevant Equations:: Please see below
How did they get y^7 in the bottom fraction?
Thank you for your reply @berkeman! I see now :)berkeman said:Multiply both the top and bottom by ##y## to help simplify the numerator...
The old saying is "close, but no cigar."Callumnc1 said:How did they get y^7 in the bottom fraction? I got their answer except I had y^6.
Thank you for your reply @Mark44!Mark44 said:The old saying is "close, but no cigar."
Obviously, you did something wrong. If we look just at the numerator of the fraction in (1), we have:
$$3x^2y^3 - 3x^3y^2(-\frac{x^3}{y^3}) = 3x^2y^3 + \frac{3x^6}y$$
So the fraction in (1) can be rewritten as $$\frac{3x^2y^3 + \frac{3x^6}y}{y^6}$$
What do you need to do to turn this complex fraction into an ordinary fraction; i.e., one that is the quotient of two polynomials?
That's not a good way to think about it. The next step from where I left off is to multiply the complex fraction by 1, in the form of ##\frac y y##. That will bump the exponent on y in the first term up top and the term in the denominator, and will clear the fraction in the second term up top. You can always multiply by 1 without changing the value of the thing that is being multiplied.Callumnc1 said:You multiply the ##3x^2y^3## and ##\frac{3x^6}{y}## by ##y## then flip the ##y^6## up
Thank you for your reply @Mark44!Mark44 said:That's not a good way to think about it. The next step from where I left off is to multiply the complex fraction by 1, in the form of ##\frac y y##. That will bump the exponent on y in the first term up top and the term in the denominator, and will clear the fraction in the second term up top. You can always multiply by 1 without changing the value of the thing that is being multiplied.
Missing out on concepts like this is why I recommended spending some time going over basic precalculus topics in another thread you posted.
Simplifying a complicated fraction involves finding the greatest common factor (GCF) of the numerator and denominator, and then dividing both by the GCF. This will result in a simplified fraction that is equivalent to the original one.
The GCF, or greatest common factor, is the largest number that divides evenly into both the numerator and denominator of a fraction. To find it, you can list out all the factors of both numbers and then identify the largest one that they have in common.
In most cases, yes. However, some fractions may already be in their simplest form. To check if a fraction can be simplified further, make sure the numerator and denominator have no common factors other than 1. If they do, you can simplify by dividing both by the common factor.
To check if you have simplified a fraction correctly, you can multiply the simplified fraction by the original denominator. If the result is the original numerator, then you have simplified the fraction correctly.
In most cases, it is not necessary to simplify a fraction. However, it can make working with fractions easier and more manageable. Additionally, some problems may require the answer to be in its simplest form, so it is important to know how to simplify fractions.