Let $$ P(x) $$ be the function $$ \frac{x}{x+1}-1 $$. Find the following: $$ P(7)=\square $$ $$ P(-4)= $$ $$ P\left(\frac{1}{10}\right)= $$ $$ P\left(-\frac{1}{3}\right)= $$ In each box, enter your answer as an integer or reduced fraction. Enter DNE for Does Not Exi Infinity.

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Let's evaluate the function $$ P(x) = \frac{x}{x+1} - 1 $$ for each given value of $$ x $$.

First, simplify $$ P(x) $$:

$$
P(x) = \frac{x}{x+1} - 1 = \frac{x - (x + 1)}{x + 1} = \frac{-1}{x + 1}
$$

So, $$ P(x) = \frac{-1}{x + 1} $$, provided that $$ x \neq -1 $$ (since division by zero is undefined).

Now, let's compute each value:

1. **$$ P(7) $$:**

$$
P(7) = \frac{-1}{7 + 1} = \frac{-1}{8} = -\frac{1}{8}
$$

2. **$$ P(-4) $$:**

$$
P(-4) = \frac{-1}{-4 + 1} = \frac{-1}{-3} = \frac{1}{3}
$$

3. **$$ P\left(\frac{1}{10}\right) $$:**

$$
P\left(\frac{1}{10}\right) = \frac{-1}{\frac{1}{10} + 1} = \frac{-1}{\frac{11}{10}} = -\frac{10}{11}
$$

4. **$$ P\left(-\frac{1}{3}\right) $$:**

$$
P\left(-\frac{1}{3}\right) = \frac{-1}{-\frac{1}{3} + 1} = \frac{-1}{\frac{2}{3}} = -\frac{3}{2}
$$

**Summary of Results:**

$$
\begin{align*}
P(7) &= -\frac{1}{8} \
P(-4) &= \frac{1}{3} \
P\left(\frac{1}{10}\right) &= -\frac{10}{11} \
P\left(-\frac{1}{3}\right) &= -\frac{3}{2}
\end{align*}
$$
$$ \begin{align*} P(7) &= -\frac{1}{8} \ P(-4) &= \frac{1}{3} \ P\left(\frac{1}{10}\right) &= -\frac{10}{11} \ P\left(-\frac{1}{3}\right) &= -\frac{3}{2} \end{align*} $$

Let \( P(x) \) be the function \( \frac{x}{x+1}-1 \). Find the following: \( P(7)=\square \) \( P(-4)= \) \( P\left(\frac{1}{10}\right)= \) \( P\left(-\frac{1}{3}\right)= \) In each box, enter your answer as an integer or reduced fraction. Enter DNE for Does Not Exi Infinity.

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