The given expression is:

$\frac{2x^2 + 7x - 3}{x^2 + 4x - 12} - \frac{2x^2 + 6x - 1}{x^2 + 4x - 12}$

Step 1: Simplify the denominator

The denominator of both terms is the same: $x^2 + 4x - 12$. We can try to factor this expression:

$x^2 + 4x - 12 = (x - 2)(x + 6)$

So, the denominators remain $(x - 2)(x + 6)$ for both fractions.

Step 2: Combine the numerators

Since the denominators are the same, we can combine the numerators:

$\frac{2x^2 + 7x - 3}{(x - 2)(x + 6)} - \frac{2x^2 + 6x - 1}{(x - 2)(x + 6)} = \frac{(2x^2 + 7x - 3) - (2x^2 + 6x - 1)}{(x - 2)(x + 6)}$

Step 3: Simplify the numerator

Now subtract the second numerator from the first:

$(2x^2 + 7x - 3) - (2x^2 + 6x - 1) = 2x^2 + 7x - 3 - 2x^2 - 6x + 1 = x - 2$

Step 4: Write the simplified expression

The simplified expression becomes:

[ \frac{x - 2}{