SOLUTION: Explain why it is necessary' to check the solution of a rational equation. State an example where it is a good thing that the solution was checked (because it mattered)

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Question 1134447: Explain why it is necessary' to check the solution of a rational equation. State an example where it is a good thing that the solution was checked (because it mattered)
Answer by mathsolverplus(88) About Me  (Show Source):
You can put this solution on YOUR website!
It is very important to check the solution of a rational equation because sometimes the solution that you obtain can actually end up being extraneous.
For example:
2%2F%28x-2%29+=+x%2F%28x-2%29
2%28x-2%29+=+x%28x-2%29
2x-4+=+x%5E2-2x
0+=+x%5E2-4x%2B4
0+=+%28x-2%29%5E2
x+=+2
However, when we substitute x = 2 back into the original equation, we see that
the denominator = 0 and WE CANNOT cannot divide by 0. Therefore, there is no solution!

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