For what positive value of x is the equation `(3)/( 2x ^(2) + 4x-6) =0` underfined ?

Explanation

To find the positive value of \( x \) for which the equation

\[ \frac{3}{2x^2 + 4x - 6} = 0 \]

is undefined, we need to set the denominator equal to zero:

### Step 1: Set the denominator to zero
\[ 2x^2 + 4x - 6 = 0 \]

### Step 2: Simplify the equation
We can factor out a 2 from the equation:
\[ 2(x^2 + 2x - 3) = 0 \]
This simplifies to:
\[ x^2 + 2x - 3 = 0 \]

### Step 3: Factor the quadratic equation
Next, we factor the quadratic:
\[ (x + 3)(x - 1) = 0 \]

### Step 4: Solve for \( x \)
Setting each factor to zero gives us:
\[ x + 3 = 0 \quad \text{or} \quad x - 1 = 0 \]
This results in:
\[ x = -3 \quad \text{or} \quad x = 1 \]

### Step 5: Identify the positive value of \( x \)
Since we are looking for the positive value of \( x \), we have:
\[ x = 1 \]

Thus, the positive value of \( x \) for which the equation is undefined is \( \boxed{1} \).

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