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dybincka [34]
3 years ago
5

What is the extraneous solution?

Mathematics
1 answer:
8_murik_8 [283]3 years ago
8 0
<h3>Answer:</h3>

  x = 1

<h3>Step-by-step explanation:</h3>

<em>The only solution is an extraneous solution</em>, which is to say the equation has no solution.

The rational expression reduces to -1 (for x≠1), which makes the equation ...

  1 = 1/x

The only solution to this is x=1, which is specifically disallowed.

___

If you subtract the right side, the equation becomes ...

  ((-x+1)(x) +2(x)(x -1) -(x -1))/(x -1) = 0

  (-x^2 +x +2x^2 -2x -x +1)/(x -1) = 0 . . . . eliminate parentheses in the numerator

  (x^2 -2x +1)/(x -1) = 0 . . . . . . . . . . . . . . . collect terms

  (x -1)^2/(x -1) = 0 . . . . . . . . . . . . . . . . . . . factor

This is undefined for the only value of x that could possibly be a solution, x=1.

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