Question 268825
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Please help me solve this equation: {{{x/(x+1))-2}}} = {{{3/(x-3)}}}
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        The solution in the post by @mananth is INCORRECT.


        His transformations, which he performs to reduce the given equation to the factored quadratic equation,

        contain a lot of arithmetic errors, and his final equation is wrong.


        The answer absents in his solution.  So, his presentation is a compote of mathematical symbols 

        with no mathematical sense,  which may lead a reader to wrong conclusion.


        Therefore,  I came to bring a correct solution.



<pre>
Your starting equation is 

    {{{x/(x+1))-2}}} = {{{3/(x-3)}}}.


The domain of this equation is the set of all real numbers except of x= -1 and x= 3.
We will work over the domain, assuming that x =/= -1  and  x =/= 3.


Multiply both sides by LCD (x+1)*(x-3) and simplify

    x*(x-3) - 2(x+1)*(x-3)  = 3(x+1),

    x^2 - 3x - 2*(x^2 +x - 3x - 3) = 3x + 3,

    x^2 - 3x - 2x^2 - 2x + 6x + 6 = 3x + 3,

    -x^2 - 2x - 3 = 0,

    x^2 + 2x + 3 = 0,

    (x+3)*(x-1) = 0.


The solutions to this equation are the numbers -3 and 1.

They both are in the domain of the given equation,

so the solution to equation (1) are  x = -3  and  x = 1.
</pre>

Solved completely and correctly.



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Here is my general impression about the solutions by @mananth at this forum.


I just learned several months ago, that @mananth systematically uses a computer code, 
which generates files with solutions.


In many cases (approximately in 10% of cases) the solutions generated by his computer code are incorrect.


But @mananth never reads and never checks what his code produces, so @mananth 
does not carry any responsibility for the quality of his solutions.


Any reader should understand it - - - @mananth does not carry any responsibility for the correctness
of his solutions: this is his principial position.


Factually, he leaves this responsibility to those tutors (like me), 
who check every, each and all his solutions totally.