explain why x+ 3/x-3 = 3+ 3/x-3 has no solution

Question

I need the answer asap

Answer 1

To be more complete, the equation should have a qualifying expression:

     x+ 3/x-3 = 3+ 3/x-3    (for x≠3)

 

This is because the equation as written may not have an undefined expression ( 3/(x-3) is undefined when x=3).

 

Now, if (3/(x-3)) were defined and we subtracted it from both sides, we would be left with x=3.  That means that an answer of x=3 can only be valid if the initial equation allows x=3; but it doesn't !!

Answer 2

Because X+3 is recipical of X-3, means they are opposite so they cancel out thats why no solution for this answer

Answer 3

You can see that 3/(x-3) is on both sides of the equation, so we an subtract it from both sides. That leaves simply  x = 3.

 

So we think we have a solution of  x = 3. So what's the trouble?

 

Let's put that 3 in place of x in the original equation.  We have  3 + 3/(3-3) = 3 + 3/(3-3).

   Can you see the trouble?  If not, then go on.

 

3 + 3/0 = 3 + 3/0

 

I hope you can see the trouble now. We know that the denominator of a fraction can't be 0.

 

So, we thought that x=3 was the solution, but we see that x isn't allowed to be 3 in the equation, so there is no solution to the equation.