Question

do not use a calculator for this item.
which value of (x) makes the following expression undefined?

\frac{15(x+3)}{-8x}

a. (\sqrt{2})
b. (-3)
c. (0)
d. (\frac{1}{8})

Explanation:

🆕 New Concept Discovered: Undefined Rational Expressions
When a fraction's denominator is zero.

Step 1: Identify the condition for an undefined expression

A rational expression (a fraction with variables) becomes undefined when its denominator is equal to \(0\), because division by zero is mathematically impossible.

For the given expression:

$$ \frac{15(x+3)}{-8x} $$

The denominator is \(-8x\).

Step 2: Set the denominator to zero and solve for \(x\)

To find the value of \(x\) that makes the expression undefined, set the denominator equal to \(0\):

$$ -8x = 0 $$

Divide both sides by \(-8\):

$$ x = \frac{0}{-8} $$

$$ x = 0 $$

Answer:

C (which is \(0\))