Respuesta :
Note: Since you have not missed to add the expression in the question. But, I am taking a general rational expression that would have 0, 6 and 9 excluded values in it. But, I would try to make sure that your concept gets cleared by my explanation.
Answer:
Let us take a rational expression as an example:
[tex]\frac{x+6}{x(x-6)(x-9)}[/tex]
⇒ x(x -6)(x -9) = 0
⇒ x = 0 or x = 6 or x = 9
The values 0, 6, and 9 are excluded from the domain of this rational expression as these values make the expression undefined.
Step by Step Explanation:
The real numbers that make the denominator of a rational expression zero are not the part of the domain of a rational expression as these values are termed as restriction values - or excluded values.
Let us take a rational expression as an example:
[tex]\frac{x+6}{x(x-6)(x-9)}[/tex]
⇒ x(x -6)(x -9) = 0
⇒ x = 0 or x = 6 or x = 9
It is clear that the real number 0, 6 and 9 would make the denominator zero, hence making the overall rational expression undefined. So, the values x=0, 6 and 9 are excluded from the domain.
The values x=0, 6 and 9 are also called restrictions.
Hence, the domain of this expression is all real numbers except 0, 6, and 9. In other words, the values 0, 6, and 9 are excluded from the domain of rational expression as these values make the expression undefined.
Keywords: domain, excluded values, rational expression
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