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question on homework question 5.25 II-A

 
 
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question on homework question 5.25 II-A
by Bober Yang - Wednesday, 15 July 2020, 10:09 AM
 

So I am reviewing the questions and the answer said to sustitutey=(3x-1)/(x^2+1)

and it said that the equation becomes y=3

i don't know how would you get that

can I get some help please thank you

 
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Re: question on homework question 5.25 II-A
by Areteem Professor - Thursday, 16 July 2020, 12:51 PM
 

Doing this substitution, the equation becomes $$y - \dfrac{3}{y} = 2,$$ which is equivalent to $$y^2 -2y-3=0.$$ This has solutions $y = 3$, and $y = -1$. So we have $$\dfrac{3x-1}{x^2+1} = 3, $$ which has no real solutions, or $$\dfrac{3x-1}{x^2+1} = -1, $$ which has solutions $x = 0$ and $x = -3$.