From the factoring, it is possible to find the following answers:
Letter A: ![\frac{x\left(x+2\right)}{x-3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5Cleft%28x%2B2%5Cright%29%7D%7Bx-3%7D)
Letter B: ![-\frac{2x^5}{\left(x^2+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)}](https://tex.z-dn.net/?f=-%5Cfrac%7B2x%5E5%7D%7B%5Cleft%28x%5E2%2B1%5Cright%29%5Cleft%28x%5E2-x%2B1%5Cright%29%5Cleft%28x%5E2%2Bx%2B1%5Cright%29%7D)
Letter C: ![x^2+y^2](https://tex.z-dn.net/?f=x%5E2%2By%5E2)
<h3>Factoring</h3>
In math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.
Here you should factor the given expression.
![\frac{x^3-4x}{x^2-5x+6} \\ \\ \frac{x\left(x+2\right)\left(x-2\right)}{x^2-5x+6}\\ \\ \frac{x\left(x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x-3\right)}\\ \\ \frac{x\left(x+2\right)}{x-3}\\ \\ Then,\\ \\ \frac{x^3-4x}{x^2-5x+6} =\frac{x\left(x+2\right)}{x-3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E3-4x%7D%7Bx%5E2-5x%2B6%7D%20%5C%5C%20%5C%5C%20%5Cfrac%7Bx%5Cleft%28x%2B2%5Cright%29%5Cleft%28x-2%5Cright%29%7D%7Bx%5E2-5x%2B6%7D%5C%5C%20%5C%5C%20%5Cfrac%7Bx%5Cleft%28x%2B2%5Cright%29%5Cleft%28x-2%5Cright%29%7D%7B%5Cleft%28x-2%5Cright%29%5Cleft%28x-3%5Cright%29%7D%5C%5C%20%5C%5C%20%5Cfrac%7Bx%5Cleft%28x%2B2%5Cright%29%7D%7Bx-3%7D%5C%5C%20%5C%5C%20%20Then%2C%5C%5C%20%5C%5C%20%5Cfrac%7Bx%5E3-4x%7D%7Bx%5E2-5x%2B6%7D%20%3D%5Cfrac%7Bx%5Cleft%28x%2B2%5Cright%29%7D%7Bx-3%7D)
Firstly, you should replace the variables A, B and C for the given expressions.
![\frac{1}{1-x+x^2}-\frac{1}{1+x+x^2}-\frac{2x}{1+x^2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1-x%2Bx%5E2%7D-%5Cfrac%7B1%7D%7B1%2Bx%2Bx%5E2%7D-%5Cfrac%7B2x%7D%7B1%2Bx%5E2%7D)
After that, you should find the least common multiple.
![\frac{\left(x^2+1\right)\left(x^2+x+1\right)}{\left(x^2+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)}-\frac{\left(x^2+1\right)\left(x^2-x+1\right)}{\left(x^2+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)}-\frac{2x\left(x^2-x+1\right)\left(x^2+x+1\right)}{\left(x^2+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cleft%28x%5E2%2B1%5Cright%29%5Cleft%28x%5E2%2Bx%2B1%5Cright%29%7D%7B%5Cleft%28x%5E2%2B1%5Cright%29%5Cleft%28x%5E2-x%2B1%5Cright%29%5Cleft%28x%5E2%2Bx%2B1%5Cright%29%7D-%5Cfrac%7B%5Cleft%28x%5E2%2B1%5Cright%29%5Cleft%28x%5E2-x%2B1%5Cright%29%7D%7B%5Cleft%28x%5E2%2B1%5Cright%29%5Cleft%28x%5E2-x%2B1%5Cright%29%5Cleft%28x%5E2%2Bx%2B1%5Cright%29%7D-%5Cfrac%7B2x%5Cleft%28x%5E2-x%2B1%5Cright%29%5Cleft%28x%5E2%2Bx%2B1%5Cright%29%7D%7B%5Cleft%28x%5E2%2B1%5Cright%29%5Cleft%28x%5E2-x%2B1%5Cright%29%5Cleft%28x%5E2%2Bx%2B1%5Cright%29%7D)
Finally, you can simplify the expression
![\frac{\left(x^2+1\right)\left(x^2+x+1\right)-\left(x^2+1\right)\left(x^2-x+1\right)-2x\left(x^2-x+1\right)\\ \\ \left(x^2+x+1\right)}{\left(x^2+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)}\\ \\ \frac{-2x^5}{\left(x^2+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)}= -\frac{2x^5}{\left(x^2+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cleft%28x%5E2%2B1%5Cright%29%5Cleft%28x%5E2%2Bx%2B1%5Cright%29-%5Cleft%28x%5E2%2B1%5Cright%29%5Cleft%28x%5E2-x%2B1%5Cright%29-2x%5Cleft%28x%5E2-x%2B1%5Cright%29%5C%5C%20%5C%5C%20%5Cleft%28x%5E2%2Bx%2B1%5Cright%29%7D%7B%5Cleft%28x%5E2%2B1%5Cright%29%5Cleft%28x%5E2-x%2B1%5Cright%29%5Cleft%28x%5E2%2Bx%2B1%5Cright%29%7D%5C%5C%20%5C%5C%20%5Cfrac%7B-2x%5E5%7D%7B%5Cleft%28x%5E2%2B1%5Cright%29%5Cleft%28x%5E2-x%2B1%5Cright%29%5Cleft%28x%5E2%2Bx%2B1%5Cright%29%7D%3D%20-%5Cfrac%7B2x%5E5%7D%7B%5Cleft%28x%5E2%2B1%5Cright%29%5Cleft%28x%5E2-x%2B1%5Cright%29%5Cleft%28x%5E2%2Bx%2B1%5Cright%29%7D)
Firstly, you should replace the variables P, Q and R for the given expressions.
![\frac{x^4-y^4}{x^2+y^2-2xy}\cdot \frac{\left(x+y\right)^2-4xy}{x^3-y^3}\div \frac{x+y}{x^2+y^2+xy}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E4-y%5E4%7D%7Bx%5E2%2By%5E2-2xy%7D%5Ccdot%20%5Cfrac%7B%5Cleft%28x%2By%5Cright%29%5E2-4xy%7D%7Bx%5E3-y%5E3%7D%5Cdiv%20%5Cfrac%7Bx%2By%7D%7Bx%5E2%2By%5E2%2Bxy%7D)
Rewriting
![\frac{\frac{x^4-y^4}{x^2+y^2-2xy}\cdot \frac{\left(x+y\right)^2-4xy}{x^3-y^3}}{\frac{x+y}{x^2+y^2+xy}}=\frac{\frac{x^4-y^4}{x^2+y^2-2xy}\cdot \frac{\left(x+y\right)^2-4xy}{x^3-y^3}\left(x^2+y^2+xy\right)}{x+y}\\ \\](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7Bx%5E4-y%5E4%7D%7Bx%5E2%2By%5E2-2xy%7D%5Ccdot%20%5Cfrac%7B%5Cleft%28x%2By%5Cright%29%5E2-4xy%7D%7Bx%5E3-y%5E3%7D%7D%7B%5Cfrac%7Bx%2By%7D%7Bx%5E2%2By%5E2%2Bxy%7D%7D%3D%5Cfrac%7B%5Cfrac%7Bx%5E4-y%5E4%7D%7Bx%5E2%2By%5E2-2xy%7D%5Ccdot%20%5Cfrac%7B%5Cleft%28x%2By%5Cright%29%5E2-4xy%7D%7Bx%5E3-y%5E3%7D%5Cleft%28x%5E2%2By%5E2%2Bxy%5Cright%29%7D%7Bx%2By%7D%5C%5C%20%5C%5C)
![\frac{\left(x^2+y^2\right)\left(x+y\right)}{x+y}=x^2+y^2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cleft%28x%5E2%2By%5E2%5Cright%29%5Cleft%28x%2By%5Cright%29%7D%7Bx%2By%7D%3Dx%5E2%2By%5E2)
Read more about the factoring here:
brainly.com/question/11579257
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The car was going about 37 miles per hour.
Answer:
1/2
Step-by-step explanation:
y2 - y1. over. x2 - x1
Well to find the range, you need to take the highest number and subtract the lowest from it:
3 - -97
3 + 97
100
Range is always positive
plz mark me as brainliest if this helped :)