Let's start by examining the given expression we need to simplify:
[tex]$
\frac{3x^4 - 2x^3 + 11}{-3x^4}
$[/tex]
We can simplify this fraction by dividing each term in the numerator by the term in the denominator:
[tex]\[
\frac{3x^4}{-3x^4} - \frac{2x^3}{-3x^4} + \frac{11}{-3x^4}
\][/tex]
Now, let's simplify each term separately:
1. Simplify the first term:
[tex]\[
\frac{3x^4}{-3x^4} = -1
\][/tex]
2. Simplify the second term:
[tex]\[
\frac{-2x^3}{3x^4} = \frac{-2}{3x}
\][/tex]
3. Simplify the third term:
[tex]\[
\frac{11}{-3x^4} = -\frac{11}{3x^4}
\][/tex]
Putting all these simplified terms together, we get:
[tex]\[
-1 + \frac{2}{3x} - \frac{11}{3x^4}
\][/tex]
Thus, the simplified form of the given expression is:
[tex]$
-\frac{3 x^4 - 2 x^3 + 11}{3 x^4}
$[/tex]
