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Question 189967: why do extraneous solutions sometimes occur for equations with rational expressions? Give an example of a rational equation in which the denominator cannot equal zero.
Is that the same thing as a problem with no solution?
i can only find information for how extraneous solutions sometimes occur for rational equations.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! why do extraneous solutions sometimes occur for equations with rational expressions?
If you raise both sides of an equation to a higher power, like square
or cube, you increase the number of solution. Some of those new
solutions may not satisfy the original equation. Those solutions are
call extraneous.
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Give an example of a rational equation in which the denominator cannot equal zero.
y = 3/x
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Is that the same thing as a problem with no solution?
No; the equation has a limited domain but has lots of solutions.
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i can only find information for how extraneous solutions sometimes occur for rational equations.
Try this:
Original equation::: x = 1
Square both sides: x^2= 1
Solve:
x^2-1 = 0
(x-1)(x+1) = 0
x = 1 or x = -1
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Test solutions in the original equation:
1 = 1 ; -1 = 1
Do you see that x=-1 is an extraneous solution?
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Cheers,
Stan H.
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