If `alpha` and `beta` are the roots of the quadratic equation `x^(2) + 3x - 4 = 0`, then `alpha^(-1) + beta^(-1) = "_____"`.

Answer

To solve the problem, we need to find the value of \( \alpha^{-1} + \beta^{-1} \) given that \( \alpha \) and \( \beta \) are the roots of the quadratic equation \( x^2 + 3x - 4 = 0 \).

### Step 1: Identify the roots of the quadratic equation
The given quadratic equation is:
\[ x^2 + 3x - 4 = 0 \]
We can factor this equation. We need two numbers that multiply to \(-4\) (the constant term) and add up to \(3\) (the coefficient of \(x\)). The numbers \(4\) and \(-1\) satisfy this condition because:
\[ 4 \times (-1) = -4 \quad \text{and} \quad 4 + (-1) = 3 \]
Thus, we can factor the equation as:
\[ (x + 4)(x - 1) = 0 \]

### Step 2: Find the roots
Setting each factor to zero gives us the roots:
\[ x + 4 = 0 \quad \Rightarrow \quad x = -4 \]
\[ x - 1 = 0 \quad \Rightarrow \quad x = 1 \]
So, the roots are:
\[ \alpha = -4 \quad \text{and} \quad \beta = 1 \]

### Step 3: Calculate \( \alpha^{-1} + \beta^{-1} \)
Now, we need to find:
\[ \alpha^{-1} + \beta^{-1} = \frac{1}{\alpha} + \frac{1}{\beta} \]
Substituting the values of \( \alpha \) and \( \beta \):
\[ \alpha^{-1} + \beta^{-1} = \frac{1}{-4} + \frac{1}{1} \]

### Step 4: Simplify the expression
Calculating this gives:
\[ \alpha^{-1} + \beta^{-1} = -\frac{1}{4} + 1 \]
To add these fractions, we convert \(1\) to a fraction with a denominator of \(4\):
\[ 1 = \frac{4}{4} \]
Now we can add:
\[ -\frac{1}{4} + \frac{4}{4} = \frac{4 - 1}{4} = \frac{3}{4} \]

### Final Answer
Thus, the value of \( \alpha^{-1} + \beta^{-1} \) is:
\[ \frac{3}{4} \]