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Simplify \(\frac{x^2+2x^4+3x^6+\dots+1005x^{2010}}{2x+4x^3+6x^5+\dots+2010x^{2009}}\)

 Aug 9, 2022

Best Answer 

 #2
avatar+2446 
+1

Factor out x from the numerator of the fraction: \(x(x + 2x^3 + 3x^5 + \cdot \cdot \cdot + 1005x^{2009})\)

 

Now, factor out 2 from the denominator: \(2(x + 2x^3 + 3x^5 + \cdot \cdot \cdot + 1005x^{2009})\)

 

So we have \({x(x + 2x^3 + 3x^5 + \cdot \cdot \cdot + 1005x^{2009}) \over 2(x + 2x^3 + 3x^5 + \cdot \cdot \cdot + 1005x^{2009})} = \color{brown}\boxed{x \over 2}\)

 Aug 9, 2022
 #1
avatar+251 
-1

Suppose that the expression equals y. 

Dividing by x gives us, (x^2 + 2x^4 +... + 1005x^(2010))/(2x^2 + 4x^4 +... + 2010x^(2010)). This gives us a value of 1/2. 

1/2 divided by x gives us \( \frac{1}{2x} \)

 Aug 9, 2022
 #2
avatar+2446 
+1
Best Answer

Factor out x from the numerator of the fraction: \(x(x + 2x^3 + 3x^5 + \cdot \cdot \cdot + 1005x^{2009})\)

 

Now, factor out 2 from the denominator: \(2(x + 2x^3 + 3x^5 + \cdot \cdot \cdot + 1005x^{2009})\)

 

So we have \({x(x + 2x^3 + 3x^5 + \cdot \cdot \cdot + 1005x^{2009}) \over 2(x + 2x^3 + 3x^5 + \cdot \cdot \cdot + 1005x^{2009})} = \color{brown}\boxed{x \over 2}\)

BuilderBoi Aug 9, 2022

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