Question 306108
<pre><font size = 4 color = "indigo"><b>
{{{x^2/(x-2)=4/(x-2)}}}

Multiply through by {{{x-2}}}

However since we are multiplying thorugh by a variable
we will have to check our answers at the end.

{{{x^2=4}}}

{{{x=""+-sqrt(4)}}}

x = ±2

We get two solutions +2 and -2, but we must check
them both in the original equation since we multiplied 
through by a variable:

Substitute +2 for x

{{{x^2/(x-2)=4/(x-2)}}}
{{{2^2/(2-2)=4/(2-2)}}}
{{{4/0=4/0}}}

Division by 0 is not defined.  So we can rule out +2

Substitute -2 for x

{{{x^2/(x-2)=4/(x-2)}}}
{{{(-2)^2/(-2-2)=4/(-2-2)}}}
{{{4/(-4)=4/(-4)}}}
{{{-1=-1}}}

So -2 is the only solution.

Edwin</pre>