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Find the domain of the rational expression: [tex]\frac{x-5}{3x-6}[/tex]

A. all real numbers except 6
B. all real numbers except 5
C. all real numbers except 0
D. all real numbers except 2

Sagot :

GinnyAnswer
To find the domain of the rational expression [tex]\(\frac{x-5}{3x-6}\)[/tex], we need to identify any values of [tex]\(x\)[/tex] that would cause the denominator to be zero, as division by zero is undefined in mathematics.

1. We start with the expression:
[tex]\[ \frac{x-5}{3x-6} \][/tex]

2. Focus on the denominator [tex]\(3x-6\)[/tex]. We need to find the values of [tex]\(x\)[/tex] that make [tex]\(3x-6=0\)[/tex].

3. Solve the equation [tex]\(3x-6=0\)[/tex]:

[tex]\[ 3x - 6 = 0 \][/tex]

To isolate [tex]\(x\)[/tex], add 6 to both sides:

[tex]\[ 3x = 6 \][/tex]

Next, divide both sides by 3:

[tex]\[ x = 2 \][/tex]

4. [tex]\(x = 2\)[/tex] is the value that makes the denominator zero. Therefore, [tex]\(x = 2\)[/tex] is excluded from the domain because it causes the expression to be undefined.

5. Hence, the domain of the rational expression [tex]\(\frac{x-5}{3x-6}\)[/tex] includes all real numbers except [tex]\(x = 2\)[/tex].

Thus, the domain is all real numbers except [tex]\(2\)[/tex]. Therefore, the correct answer is:

- All real numbers except 2
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