Sure! Let's go through the simplification of the mathematical expression:
Given the expression:
[tex]\[
\frac{3 - 4x}{2 + 3x - 2x^2}
\][/tex]
### Step-by-Step Simplification
1. Identify the numerator and the denominator:
- Numerator: [tex]\( 3 - 4x \)[/tex]
- Denominator: [tex]\( 2 + 3x - 2x^2 \)[/tex]
2. Simplification of the expression:
- In our case, both the numerator and the denominator are already simplified polynomials.
3. Check for common factors:
- To simplify [tex]\(\frac{3 - 4x}{2 + 3x - 2x^2}\)[/tex], we should check for any common factors between the numerator and the denominator. However, in this case, there are no common factors that we can factor out.
4. Result:
- Since there are no common factors to further simplify the expression, the given fraction is already in its simplest form.
In conclusion, the simplified form of the given expression:
[tex]\[
\frac{3 - 4x}{2 + 3x - 2x^2}
\][/tex]
Remains as it is:
[tex]\[
\frac{3 - 4x}{-2x^2 + 3x + 2}
\][/tex]
