Question

Solve the equation Upper P equals n plus k plus mP=n+k+m for nn.
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Part 1
nnequals=enter your response here ​(Simplify your​ answer.)

Answer 1

To solve the equation \( P = n + k + mP = n + k + m \), we can first rewrite it in a more manageable form. This equation suggests that there are two expressions for \( P \):

1. \( P = n + k + mP \)
2. \( P = n + k + m \)

From the second expression, we have:

\[
P - mP = n + k
\]

This simplifies to:

\[
P(1 - m) = n + k
\]

Assuming \( m \neq 1 \), we can solve for \( P \):

\[
P = \frac{n + k}{1 - m}
\]

Now, we can substitute \( P \) back into the first equation:

\[
\frac{n + k}{1 - m} = n + k + m\left(\frac{n + k}{1 - m}\right)
\]

We can simplify this equation, but it's already quite involved. To more directly isolate \( n \), we note that your question is asking for \( n \) specifically. Given the initial format, it seems we are aiming to express \( n \) in terms of \( P, k, \) and \( m \).

Starting from the assumption \( P = n + k + m \):

1. Rearranging this equation gives:

\[
n = P - k - m
\]

This provides a straightforward formula for \( n \):

\[
n = P - k - m
\]

If there are specific numeric values for \( P, k, \) or \( m \), please provide them so we can compute a numerical value for \( n \). Otherwise, the simplified answer for \( n \) in terms of \( P, k, m \) is:

\[
n = P - k - m
\]