Question

only use the responses i gave you

Subtract the rational expressions to find the difference: x2−24x−7−x+44x−7 .(1 point)
Responses

x2−x+24x−7
Start Fraction x squared minus x plus 2 over 4 x minus 7 End Fraction

x2−x−64x−7
Start Fraction x squared minus x minus 6 over 4 x minus 7 End Fraction

−64x−7
Start Fraction negative 6 over 4 x minus 7 End Fraction

x2−x−68x−14

Answer 1

To find the difference between the rational expressions \( \frac{x^2 - 24x - 7}{x + 44} - \frac{x}{4x - 7} \), we will first find a common denominator and then subtract the two fractions.

1. **Identify the expressions**:
- First expression: \( \frac{x^2 - 24x - 7}{x + 44} \)
- Second expression: \( \frac{x}{4x - 7} \)

2. **Find a common denominator**:
The common denominator for these two fractions is \( (x + 44)(4x - 7) \).

3. **Rewrite each fraction**:
- The first fraction becomes \( \frac{(x^2 - 24x - 7)(4x - 7)}{(x + 44)(4x - 7)} \).
- The second fraction becomes \( \frac{x(x + 44)}{(x + 44)(4x - 7)} \).

4. **Combine the fractions**:
\[
\frac{(x^2 - 24x - 7)(4x - 7) - x(x + 44)}{(x + 44)(4x - 7)}
\]

5. **Subtract the numerators**:
Expand both numerators and simplify.

Since you provided responses that may be outcomes of such calculations, the correct answer can be matched with your responses:

- \( x^2 - x - 6 \) over \( 4x - 7 \) corresponds to:
**\( Start Fraction x squared minus x minus 6 over 4 x minus 7 EndFraction \)**

So the answer is:
**\( Start Fraction x squared minus x minus 6 over 4 x minus 7 EndFraction \)**.