Question

Subtract the rational expressions to find the difference: x^2−2/4x−7−x+4/4x−7
.(1 point)
Responses

−6/4x−7
Start Fraction negative 6 over 4 x minus 7 End Fraction

x^2−x−6/4x−7
Start Fraction x squared minus x minus 6 over 4 x minus 7 End Fraction

x^2−x+2/4x−7
Start Fraction x squared minus x plus 2 over 4 x minus 7 End Fraction

x^2−x−6/8x−14
Start Fraction x squared minus x minus 6 over 8 x minus 14 End Fraction
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Answer 1

To subtract the rational expressions \( \frac{x^2 - 2}{4x - 7} - \frac{x + 4}{4x - 7} \), we can combine them since they have a common denominator.

1. **Combine the numerators:**
\[
\frac{x^2 - 2 - (x + 4)}{4x - 7}
\]

2. **Simplify the numerator:**
\[
x^2 - 2 - x - 4 = x^2 - x - 6
\]

3. **Writing the final expression:**
\[
\frac{x^2 - x - 6}{4x - 7}
\]

Thus, the result of the subtraction \( \frac{x^2 - 2}{4x - 7} - \frac{x + 4}{4x - 7} \) is:

\[
\frac{x^2 - x - 6}{4x - 7}
\]

The correct answer from the options provided is:

**x^2−x−6/4x−7** (Start Fraction x squared minus x minus 6 over 4 x minus 7 End Fraction)