Question 1209876
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Polynomials-and-rational-expressions/1209876: Find the largest value of x where the plots of
f(x) = - \frac{2x + 5}{x + 3} and g(x) = \frac{12}{x - 1}
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Be aware !


The answer in the post by @CPhill is incorrect.


He made an arithmetic error while calculated the discriminant of the quadratic equation.


The discriminant is NEGATIVE, which means that the quadratic equation does not have real solutions.


The answer is that the plots of these given functions do not intersect in real domain.



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                Regarding the post by @CPhill . . . 



Keep in mind that @CPhill is a pseudonym for the Google artificial intelligence.


The artificial intelligence is like a baby now. It is in the experimental stage 
of development and can make mistakes and produce nonsense without any embarrassment.



                It has no feeling of shame - it is shameless.



This time, again,  it made an error.



Although the @CPhill' solutions are copy-paste  Google  AI solutions,  there is one essential difference.


Every time,  Google  AI  makes a note at the end of its solutions that  Google  AI  is experimental
and can make errors/mistakes.


All @CPhill' solutions are copy-paste of  Google  AI  solutions, with one difference:
@PChill never makes this notice and never says that his solutions are copy-past that of Google.
So,  he  NEVER  SAYS  TRUTH.


Every time,  @CPhill embarrassed to tell the truth.

But I am not embarrassing to tell the truth,  as it is my duty at this forum.



And the last my comment.


When you obtain such posts from @CPhill,  remember,  that  NOBODY  is responsible for their correctness, 
until the specialists and experts will check and confirm their correctness.


Without it,  their reliability is  ZERO and their creadability is  ZERO,  too.



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In his post, @greenestamps presented a result,  different from mine.


It is because,  by mistake,  he solved  DIFFERENT  equation than it is given in the original post.


In the original post,  the equations/functions were 


        f(x) = {{{-(2x + 5)/(x + 3)}}}   and   g(x) = {{{12/(x - 1)}}}.



In his post,  @greenestamps mistakenly used functions


        f(x) = {{{(2x + 5)/(x + 3)}}}   and   g(x) = {{{12/(x - 1)}}}.



Notice that his function  f(x)  has the opposite sign,  comparing with the given function  f(x).


Therefore,  it is no wonder that he came to different answer,  comparing with mine.



Thus my conclusion remains unchangeable:



    ******************************************************************


        the solution and the answer in the post by @CPhill both are incorrect.


    ******************************************************************



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In the post by  Edwin,  he made the same error,  which @greenestamps made in his post.


Edwin plotted function    f(x) = {{{(2x+5)/(x+3)}}},    while in the original problem the given function is with the opposite sign   f(x) = {{{-(2x+5)/(x+3)}}}.


So,  it is not wonder that using wrong function,  Edwin got wrong answer.



For your convenience, I prepared the plot of the given functions.   It is shown under this link


<A HREF=https://www.desmos.com/calculator/dog5dqdqlc>https://www.desmos.com/calculator/dog5dqdqlc</A> 


https://www.desmos.com/calculator/dog5dqdqlc


In addition to my algebraic explanations in my post above, &nbsp;this plot clearly shows visually 
that there no any intersection/intersections between the plots of the given functions.