To resolve the fraction \(\frac{3}{x^2 + x - 2}\) into partial fractions, we need to factor the denominator and then find the appropriate constants for the partial fractions.

The denominator \(x^2 + x - 2\) can be factored as \((x - 1)(x + 2)\).

Now, we can express the fraction as a sum of two partial fractions with unknown constants \(A\) and \(B\):

\(\frac{3}{x^2 + x - 2} = \frac{A}{x - 1} + \frac{B}{x + 2}\)

To find the values of \(A\) and \(B\), we can clear the fractions by multiplying both sides of the equation by the common denominator \((x - 1)(x + 2)\):

\[3 = A(x + 2) + B(x - 1)\]

Now, substitute values of \(x\) that make the terms with \(A\) or \(B\) disappear:

For \(x = 1\):

\[3 = A(1 + 2) + B(1 - 1)\]

\[3 = 3A\]

\[A = 1\]

For \(x = -2\):

\[3 = A(-2 + 2) + B(-2 - 1)\]

\[3 = -3B\]

\[B = -1\]

Now that we have found the values of \(A\) and \(B\), we can write the partial fraction decomposition:

\(\frac{3}{x^2 + x - 2} = \frac{1}{x - 1} - \frac{1}{x + 2}\)