can someone teach me how to get the common term (the numeric) from this equation:

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can someone teach me how to get the common term (the numeric) from this equation:

Mathematics
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Equation is attached
1 Attachment
first look at the coefficients: 1/2, -3/2,-1/2 i can divide 1/2 evenly into all 3 next look at the exponents of the variable x k,2k,3k i can take at most 1 k away from each of them so we factor out 1/2x^k leaving 1/2x^k(1-3x^k-x^2k)
Can you give me another example please?

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I understand the part related to the exponents. The fraction coefficients is what im confussed in
3/4x^2 - 3/2x^3 +1/4x^4 coefficients: 3/4, -3/2, 1/4 try to break them down into lowest fractions 3/4 = 3*1/4 3/2 = 3*1/2 = 6*1/4 1/4 = 1*1/4 now they all have something in common, the 1/4 exponents: 2,3,4 i can take away at most 2 from each exponent factor out 1/4x^2 =1/4x^2(3 - 6x +x^2)
Ok it is clear for me now. One medal for you help. Thank you friend :)
no problem :)

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