Set the denominator equal to zero.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find when the expression $\frac{5x+3}{6x(x+1)}$ will be undefined, we need to determine the values of $x$ that make the denominator equal to zero.
Step 1: Set the denominator equal to zero.
$$6x(x+1) = 0$$
Step 2: Solve for $x$.
For the product of terms to be zero, at least one of the terms must be zero.
So, either $6x = 0$ or $x+1 = 0$.
Step 3: Solve each equation for $x$.
For the first case:
$$6x = 0$$
$$x = \frac{0}{6}$$
$$x = 0$$
For the second case:
$$x+1 = 0$$
$$x = -1$$
Therefore, the expression is undefined when $x = 0$ or $x = -1$.
The set of values for $x$ is $\{0, -1\}$.
Comparing this with the given options:
A. $\{-3, 0\}$
B. $\{-3, -1\}$
C. $\{0, -1\}$
D. $\{0, 1\}$
The correct option is C.
The final answer is $\boxed{\text{C. } \{0, -1\}}$.
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