Question 264797: a^2/a-3 = 9/a-3
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949)   (Show Source):
Answer by ikleyn(53742)  (Show Source):
You can put this solution on YOUR website! .
a^2/a-3 = 9/a-3
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The solution by @mananth in his post is FATALLY WRONG.
See my correct solution below.
Your original equation is
 =  .
Its domain is the set of all real numbers except of 'a = 3', where the denominator is zero
and expressions on the left side and the right side are not defined.
So, we will look for the solution (a solution) in the domain, excluding a = 3.
In the domain, multiply both sides by (a-3). You will get an equivalent equation in the domain
a^2 = 9,
which gives two possible solutions
a = 3 and a = -3.
But a = 3 is a prohibited value, while a = -3 works perfectly.
?ANSWER. The solution to the given equation is a = -3.
This solution is UNIQUE: there is NO other solution.
Solved correctly.
This problem is a TRAP, and @mananth felt in this trap, inviting you, the reader, to follow him.
My task is to teach you to recognize such traps and to avoid them.
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