Question 630229: How do I solve this equation?
((x/(x-2)) -5 = ((2/(x-2))
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! 
There are several ways to solve equations like this. I think the easiest method starts with eliminating the fractions. Fractions can be eliminated by multiplying both sides of the equation by the lowest common denominator (LCD) of all the fractions on both sides of the equation.
Since both denominators are the same, x-2, the LCD is easy to find. So we will multiply both sides by x-2:
On the right side, the x-2's cancel. On the left side we need to use the Distributive Property:
The x-s'2 cancel in the first part of the left side. With the rest of the left side we multiply it out, being careful to keep the minus in front:
which simplifies further to:
This is now a very easy equation to solve. Subtracting 10 from each side:
Dividing by -4:
Now we check our solution. This is not optional! When we multiplied both sides by the LCD, x-2, we multiplied both sides by something that could be zero. It is not wrong to do this. But when you do you are required to check your answer(s) because they may not actually work!
Use the original equation to check:
Checking x = 2:
As we can see, we have denominators of zero. Since dividing by zero is undefined, this solution fails the check! So we must reject/discard it. And since this was the only "solution" we found: Your equation has no solutions! (IOW, it can never be true, no matter what number x is!)
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