Question

Simplify (-8r^4+4r)divided by 6r^3

Answer 1

To simplify the expression \((-8r^4 + 4r) \div 6r^3\), we can break it down step by step.

1. **Distribute the division**: We can rewrite the division as follows:

\[
\frac{-8r^4 + 4r}{6r^3} = \frac{-8r^4}{6r^3} + \frac{4r}{6r^3}
\]

2. **Simplify each term separately**:

- For the first term:

\[
\frac{-8r^4}{6r^3} = \frac{-8}{6} \cdot \frac{r^4}{r^3} = \frac{-4}{3} \cdot r^{4-3} = \frac{-4}{3}r
\]

- For the second term:

\[
\frac{4r}{6r^3} = \frac{4}{6} \cdot \frac{r}{r^3} = \frac{2}{3} \cdot r^{1-3} = \frac{2}{3} \cdot r^{-2} = \frac{2}{3r^2}
\]

3. **Combine the simplified terms**:

Putting it all together, we have:

\[
\frac{-4}{3}r + \frac{2}{3r^2}
\]

The final simplified expression is:

\[
\frac{-4}{3}r + \frac{2}{3r^2}
\]