In solving a rational equation, we always clear of fractions.

When we clear of fractions we always multiply both sides by a
variable quantity.

When we multiply both sides of an equation by a variable expression,
we may introduce an extraneous solution a zero of that expression 
we multiplied through by.   

Example:



The LCD is 
  
So we multiply through by 

















So at first it appears that  is
a solution.  However when we check:









But there are zeros in two denominators!

So there is no solution to this rational equation.

Edwin