<PRE><B>Question 1206414</B>
&lt;pre&gt;
Question: sqrt(x)-sqrt(3x-3)=1

My work: 
sqrt(x)-sqrt(3x-3)=1
(sqrt(x))^2=(1+sqrt(3x-3))^2
x=(1+sqrt(3x-3))(1+sqrt(3x-3))
x=1+sqrt(3x-3)+sqrt(3x-3)+(sqrt(3x-3))^2
x=3x-2+2(sqrt(3x-3))
(-2x+2)/2=2(sqrt(3x-3))/2
(-x)^2=(sqrt(3x-3))^2
x^2=3x-3
0=x^2+3x-3
After this step, I get lost. I know the answer is supposed to be 1 but I am not sure where I went wrong or where to go from the last step I took.

Question: sqrt(x)-sqrt(3x-3)=1
          {{{matrix(10,3, sqrt (x) - sqrt (3x - 3), &quot;=&quot;, 1, sqrt (x), &quot;=&quot;, 1 + sqrt (3x - 3), (sqrt(x))^2, &quot;=&quot;, (1 + sqrt(3x - 3))^2, x, &quot;=&quot;, (1 + sqrt(3x - 3))(1 + sqrt (3x - 3)), x, &quot;=&quot;, 1 + sqrt(3x - 3) + sqrt(3x - 3) + (sqrt(3x-3))^2, x, &quot;=&quot;, 3x - 2 + 2(sqrt(3x - 3)), x - 3x + 2, &quot;=&quot;, 2(sqrt(3x - 3)), - 2x + 2, &quot;=&quot;, 2(sqrt(3x - 3)), (- 2x + 2)/2, &quot;=&quot;, 2(sqrt(3x - 3))/2, - x + 1, &quot;=&quot;, sqrt(3x - 3))}}}
                {{{matrix(1,3, (- x)^2, &quot;=&quot;, (sqrt(3x - 3))^2)}}} &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;&lt;===== ERROR IS HERE!!&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;
             {{{matrix(1,3, (- x + 1)^2, &quot;=&quot;, (sqrt(3x - 3))^2)}}} &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;&lt;===== s/b THIS, instead!&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;
     {{{matrix(3,3, x^2 - 2x + 1, &quot;=&quot;, 3x - 3, x^2 - 2x + 1 - 3x + 3, &quot;=&quot;, 0,               x^2 - 5x + 4, &quot;=&quot;, 0)}}}
     (x - 1)  (x - 4) = 0
x - 1 = 0   |   x - 4 = 0 ---- Equating each factor to 0
    x = 1   |       x = 4

                        &lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;&lt;u&gt;C H E C K&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;&lt;/u&gt;
      &lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;&lt;u&gt;x = 1&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;&lt;/u&gt;                               &lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;&lt;u&gt;x = 4&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;&lt;/u&gt;
{{{matrix(5,3, sqrt (x) - sqrt (3x - 3), &quot;=&quot;, 1,
sqrt (1) - sqrt(3(1) - 3), &quot;=&quot;, 1,
sqrt (1) - sqrt (3 - 3), &quot;=&quot;, 1,
sqrt (1) - sqrt(0), &quot;=&quot;, 1,
1 - 0, &quot;=&quot;, 1)}}}                  {{{matrix(5,3, sqrt (x) - sqrt (3x - 3), &quot;=&quot;, 1,
sqrt (4) - sqrt(3(4) - 3), &quot;=&quot;, 1,
sqrt (4) - sqrt (12 - 3), &quot;=&quot;, 1,
sqrt (4) - sqrt(9), &quot;=&quot;, 1,
2 - 3, &quot;=&quot;, 1)}}}
             &lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;1 = 1 (TRUE)                &lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;- 1 = 1 (FALSE)
          x = 1 is the &lt;u&gt;ONLY SOLUTION&lt;/u&gt;&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;     x = 4 is an &lt;u&gt;EXTRANEOUS SOLUTION&lt;/u&gt;&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;&lt;/pre&gt;</PRE>