Question 549568: Hello! I wish I could say that I started on this problem but I have no clue what to do. Here is the problem 10/3x-8=2/x. Can you please help?
Found 2 solutions by josmiceli, KMST:
Answer by josmiceli(19441)   (Show Source):
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! EDIT:
So it was really  . I apologize. I always try to understand what the question was meant to be, even when something different was inadvertently said, but I failed this time.
Too bad that you could not type one horizontal line with the 10 on top and 3x-8 below the line. In algebra, 10/3x-8 typed on one single line would probably be interpreted as  by eople who remember the rules for order of operations. Another possible interpretation is  . That's how most calculators would interpret it, if you entered a number for x. I've known analytical chemists who got lots of grief from similar misunderstanding with their calculators.
The problem is that the very useful horizontal line (fraction bar, vinculum, or whatever you call it) comes with two sets of invisible parenthesis: one encasing what's above the line, and the other encasing what's below the line. The slanted line has no parentheses attached, and without those parentheses the expression has a different meaning.
If you type it as 10/(3x-8), calculators and people who believe in order of operations rules would understand  .
From , you could try to eliminate denominators by multiplying both sides of the equal sign by one denominator at a time, or by both if you are in a hurry. I am in a hurry.
-->  -->  -->  --> 
On multiplying by an expression that could be zero for some x, we may be introducing some extraneous solution, but we will discard any we introduce when we verify at the end.
-->  -->  --> 
Verifying:
It checks out. is the solution.
PS I do not know if it's an option for entering questions, but I enter 10/(3x-8) between three "{" and "}}}" and the website displays it as . It even lets me preview my post by clicking on a "Preview your answer" button, to make sure my answer is displayed the way I want it.
= ? (If that's not it, I'll try another one below)
You get to the solution in many small steps. There is no single correct path to the solution. I'll just show you one way.
-->  (add 8 to both sides)
-->  (subtract 2/x from both sides)
-->  -->  (get common denominator, add fractions)
-->  (multiply both sides by 3x)
-->  --->  (simplify, re-arranging, re-associating factors)
-->  --> 
 ? If so, read on. If not, ignore what follows.
Let's multiply both sides times x to get
 --> 
Now let's multiply both sides by 3 to get
Applying the quadratic formula, we get
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