To divide and simplify the given expression, follow these steps:
1. Write down the original expression:
[tex]\[
\frac{24 u^4 + 26 u^3}{3 u^3}
\][/tex]
2. Separate the numerator and denominator:
[tex]\[
\frac{24 u^4}{3 u^3} + \frac{26 u^3}{3 u^3}
\][/tex]
3. Simplify each fraction separately:
- For the first fraction:
[tex]\[
\frac{24 u^4}{3 u^3} = \frac{24}{3} \cdot \frac{u^4}{u^3}
\][/tex]
Simplify the constants:
[tex]\[
\frac{24}{3} = 8
\][/tex]
Simplify the powers of [tex]\( u \)[/tex]:
[tex]\[
\frac{u^4}{u^3} = u^{4-3} = u
\][/tex]
So, the first fraction simplifies to:
[tex]\[
8u
\][/tex]
- For the second fraction:
[tex]\[
\frac{26 u^3}{3 u^3} = \frac{26}{3} \cdot \frac{u^3}{u^3}
\][/tex]
Since [tex]\( u^3/u^3 = 1 \)[/tex]:
[tex]\[
\frac{26}{3} \cdot 1 = \frac{26}{3}
\][/tex]
4. Combine the simplified fractions:
[tex]\[
8u + \frac{26}{3}
\][/tex]
Thus, the simplified expression is:
[tex]\[
8u + \frac{26}{3}
\][/tex]
This is the simplified form of the given expression.
