Expert: Bobby Soltani - 7/12/2005

Question
Hello:


One method used to solve the following equation is to multiply both sides of the equation by the denominator x from 3/x.

3/x - 1 = 2

(x) 3/x - 1 = 2 (x) = 3 - 1 = 2x
This now becomes 2 = 2x
Now divide by 2: 2/2 = 2x/2 = 1 = x
Answer: 1

My question is why is the -1  from 3/x - 1  not multiplied by x?  Is 3/x - 1 regarded as one complete term? If so, why?

I thank you for your reply.  

Answer
Hi,

The method you used to solve the equation is incorrect.  It is just a coincidence that you get the correct answer for that particular problem.  The correct way to solve the problem is:
3/x - 1 = 2
add 2
3/x = 3
multiply by x
3 = 3x
divide by 3
x = 1

To answer your question, the -1 should be multiplied by the x.

x(3)/x - x = 2x
3 = 3x
x = 1

Let me know if you have any questions.

Bobby