Question 23695
Multiply both sides of the equation by the LCD which is (x-3)


{{{1/(x-3)+ 7 = x/(x-3)}}}

{{{(x-3)*(1/(x-3))+ 7*(x-3)  =(x-3)*( x/(x-3))}}}


The x-3 divides out in the first and last fractions leaving :


{{{1 + 7(x-3) = x}}}
{{{1+7x -21 = x}}}
{{{7x - 20 = x}}}


Add +20 to each side:
{{{7x -20+ 20 = x+ 20}}}
{{{7x=  x+20}}}


Now, subtract x from each side:
{{{7x - x = x+20 -x}}}
{{{6x= 20}}}


Divide by 6:

{{{(6x)/x = 20/6}}}


Reduce the fraction:

{{{x = 10/3}}}


Check to make sure no denominators are zero.  The answer is acceptable.


R^2 at SCC