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Math  /  Algebra

QuestionFor which values of x is the expression undefined? x2−166x−6\frac{x^{2}-16}{6 x-6}
Answer (†) Additional Solution No Solution x=x= □\square Submit Answer

Studdy Solution

STEP 1

1. The expression x2−166x−6\frac{x^2 - 16}{6x - 6} is a rational function.
2. A rational function is undefined where its denominator is zero.
3. We need to find the values of xx that make the denominator zero.

STEP 2

1. Identify the denominator of the expression.
2. Set the denominator equal to zero and solve for xx.
3. Verify the solution(s) to ensure they make the denominator zero.

STEP 3

Identify the denominator of the expression:
The denominator of x2−166x−6\frac{x^2 - 16}{6x - 6} is 6x−66x - 6.

STEP 4

Set the denominator equal to zero and solve for xx:
6x−6=0 6x - 6 = 0
Add 6 to both sides:
6x=6 6x = 6
Divide both sides by 6:
x=1 x = 1

STEP 5

Verify the solution to ensure it makes the denominator zero:
Substitute x=1x = 1 back into the denominator:
6(1)−6=6−6=0 6(1) - 6 = 6 - 6 = 0
Since the denominator is zero when x=1x = 1, the expression is undefined at this value.
The expression is undefined for x=1x = \boxed{1}.

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