Question 703767: x+3 4
----- = -----
6 x-2
Find x
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! First, we get rid of denominators:
 --> 
The justification for that step can be stated as
"multiplying both sides of the equal sign times 6(x-2)" or as
"equating the cross-products".
Then we multiply:
-->  --> 
Subtracting 24 from both sides, we get our quadratic equation:
-->  --> 
We can solve it by factoring if we can see that
because then we can write it as
 and see that the solutions are
 which makes  and
 which makes 
At this point we need to verify, by substituting
For x=-6:
 and
the solution verifies.
For x=5:
 and
the solution verifies too.
We need to verify because in the first step, when we got rid of denominators,
we could have ended with an equation not quite equivalent.
The new equation could have had extra solutions, called "extraneous solutions".
Rather than worry about extraneous solutions at front, we just verify at the end.
Verifying finds mistakes in the calculations, and lets us find (and discard) extraneous solutions.
NOTE:
can also be written as (x+3)/6 = 4/(x-2)
The horizontal fraction bars are grouping symbols, meaning that the expressions above and below the bar have to be calculated first (as if they were inside parentheses).
When we can only type a line at a time, as in entering a calculation into a calculator, we must include the brackets to indicate the same thing.
To calculate  ,
if you type (-6+3)/6 into a calculator, you get (-3)/6=-0.5, which is what you wanted.
If you type -6+3/6 , you get 
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