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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}{

Simplify the expression: (2x^2 + 7x - 3) / (x^2 + 4x - 12) - (2x^2 + 6x - 1) / (x^2 + 4x - 12)

Learn how to simplify rational expressions involving quadratic numerators and denominators. This step-by-step solution explains how to factor quadratic expressions and subtract fractions with common denominators, suitable for students in Grades 9-12.

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