<PRE><B>Question 133919</B>
Well first you need to get a common denominator.  Since 2/3 of the fractions have a denominator of x-1 that will be your common denominator.  So multiply everything by x-1 and the denominator cancles off leaving you with.&lt;br&gt;

x+x(x-1)=4x-3&lt;br&gt;

now just solve:&lt;br&gt;
x+x(x-1)=4x-3 --&gt; Distribute the x
x + x^2 - x = 4x - 3 --&gt; Collect like terms on left hand side
x^2 - 4x + 3 = 0 --&gt; Factor
(x-1)(x-3) = 0 --&gt; Set each factor equal to zero and solve
x = 1 and x = 3&lt;br&gt;

Now lets check our solutions &lt;br&gt;

x/x-1 + x = 4x-3/x-1&lt;br&gt;

when x = 1 you get &lt;br&gt;

1/1-1 + 1 = 4-3/1-1 well since you can&#39;t divide by zero we know that x = 1 is a extraneous answer.&lt;br&gt;

when x = 3 you get &lt;br&gt;

3/3-1 + 3 = 4(3)-3/3-1 
3/2 + 3 = 12-3/2
3/2 + 3 = 9/2
9/2 = 9/2 &lt;br&gt;

that one checks out.  </PRE>