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(2x+1)/(x^(2)-1)+(x)/(x^(2)-3x+2)=4

 Jul 16, 2017
 #1
avatar+95175 
+2

(2x+1)/(x^(2)-1)+(x)/(x^(2)-3x+2)=4

 

I'll try and make sense of your question first

 

\(\frac{(2x+1)}{(x^{2}-1)}+\frac{(x)}{(x^{2}-3x+2)}=4\qquad x\ne\pm1\\ \frac{(2x+1)}{(x-1)(x+1)}+\frac{(x)}{(x-2)(x-1)}=4 \qquad x\ne\pm1,\quad x\ne2\\ \frac{(2x+1)(x-2)}{(x-1)(x+1)(x-2)}+\frac{(x)(x+1)}{(x-2)(x-1)(x+1)}=4\\ (2x+1)(x-2)+(x)(x+1)=4(x-1)(x+1)(x-2)\\ 2x^2-4x+x-2+x^2+x=4(x-1)(x+1)(x-2)\\ 3x^2-3x+x-2=(x-2)(4x^2-4)\\ 3x^2-2x-2=4x^3-4x-8x^2+8\\ 0=4x^3-4x+2x-8x^2-3x^2+8+2\\ 0=4x^3-11x^2-2x+10\\ \)

 

Here is the approximate answers

https://www.wolframalpha.com/input/?i=4x%5E3-11x%5E2-2x%2B10%3D0

 Jul 16, 2017
 #2
avatar
+1

Thank you. I'm having doubts about my answer but now I see where I am wrong

Guest Jul 16, 2017
 #3
avatar+27336 
+2

This should help you visualize the equation:

 

.

 Jul 16, 2017

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