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Simplify the division:

[tex]\[
\frac{20 - 15m + 5m^3 - m^5}{-5m}
\][/tex]


Sagot :

Sure, let's solve the division problem step-by-step.

We need to simplify the expression:

[tex]\[ \frac{20 - 15m + 5m^3 - m^5}{-5m} \][/tex]

Let's divide each term in the numerator by [tex]\(-5m\)[/tex].

1. Divide [tex]\(20\)[/tex] by [tex]\(-5m\)[/tex]:

[tex]\[ \frac{20}{-5m} = -\frac{20}{5m} = -\frac{4}{m} \][/tex]

2. Divide [tex]\(-15m\)[/tex] by [tex]\(-5m\)[/tex]:

[tex]\[ \frac{-15m}{-5m} = \frac{15m}{5m} = 3 \][/tex]

3. Divide [tex]\(5m^3\)[/tex] by [tex]\(-5m\)[/tex]:

[tex]\[ \frac{5m^3}{-5m} = -\frac{5m^3}{5m} = -m^2 \][/tex]

4. Finally, divide [tex]\(-m^5\)[/tex] by [tex]\(-5m\)[/tex]:

[tex]\[ \frac{-m^5}{-5m} = \frac{m^5}{5m} = \frac{m^4}{5} \][/tex]

Now, combine all these results together:

[tex]\[ -\frac{4}{m} + 3 - m^2 + \frac{m^4}{5} \][/tex]

Rewriting in a simpler form, we get:

[tex]\[ \frac{m^4}{5} - m^2 + 3 - \frac{4}{m} \][/tex]

Thus, the final simplified result of the division is:

[tex]\[ \boxed{\frac{m^4}{5} - m^2 + 3 - \frac{4}{m}} \][/tex]
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