Question 993911
.
{{{2+5/(x-4)}}} = {{{(x+1)/(x-4)}}}.


Multiply both sides by (x-4).


You will get


2*(x-4) + 5 = x+1.


Simplify:


2x - 8 + 5 = x + 1.


x = 4.


But  x = 4  is prohibited,  because the original equation has  (x-4)  in the denominators.  It is prohibited to divide by zero.


Thus the equation has no solutions.


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{{{graph( 330, 330, -10.5, 10.5, -10.5, 10.5,
          2+5/(x-4) - (x+1)/(x-4)
)}}}


The plot of {{{2+5/(x-4) - (x+1)/(x-4)}}}

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</TABLE>