Question 268825: Please help me solve this equation: 
Found 4 solutions by mananth, jsmallt9, ikleyn, n2:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! x/(x+1)-2=3/(x-3)
x-2x-2 = 3(x+1)/(x-3)
-x-2= 3x+3 /x-3
(x-3(-x-2)= 3x+3
-x^2-2x+3x+6=3x+3
-x^2-2x+3=0
x^2-2x-3=0
x^2-3x+x-3=0
x(x-3)+1(x-3)=0
(x-3)(x+1)=0
Answer by jsmallt9(3759)  (Show Source):
Answer by ikleyn(53712)  (Show Source):
You can put this solution on YOUR website! .
Please help me solve this equation:  = 
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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.
Your starting equation is
= .
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.
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.
Answer by n2(72) (Show Source):
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