Select the domain of the following fraction:
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Select the domain of the following fraction:
The domain depends on the denominator and we can see that there is no variable in the denominator.
Therefore, the domain is all numbers.
All numbers
\( 2x+\frac{6}{x}=18 \)
What is the domain of the above equation?
The number 5 is a constant that never changes! Since 5 ≠ 0, the fraction is always defined for any value of x.
Only when the denominator contains a variable that could make it equal zero. For example, is undefined when x = 2.
Set the denominator equal to zero and solve: if denominator is x - 4, then x - 4 = 0, so x = 4 must be excluded from the domain.
No! The numerator can equal zero (that just makes the whole fraction equal zero), but it never restricts the domain. Only worry about the denominator.
It means you can substitute any number for x and the expression will have a real value. There are no restrictions or excluded values.
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