Question 1076669
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<pre>
The equation is 

{{{((x+3)/(x-1))^2}}} = {{{(2x+9)/(2x-6)}}}.     (1)
</pre>


The solution by "josgarithmetic" is {{{highlight(WRONG)}}}.



{{{graph( 330, 330, -7.5, 12.5, -2.5, 4.5,
          ((x+3)/(x-1))^2, (2x+9)/(2x-6)
)}}}


Plots y = {{{((x+3)/(x-1))^2}}} (red)  and y = (2x+9)/(2x-6) green)


<pre>
To solve (1), cross-multiply and simplify.

You will get the quadratic equation 

{{{x^2 - 2x - 63}}} = 0.


It has the solution  {{{x[1,2]}}} = {{{(2 +- sqrt(4+4*63))/2}}} = {{{(2 +- 16)/2}}}


The only positive solution for x (which works) is  x = {{{(2 +
 16)/2}}} = 9.
</pre>