The following table gives the price per unit for different volume purchases.
\begin{tabular}{|c|c|c|c|c|c|}
\hline No, bought $(x)$ & 4 & 5 & 6 & 7 & 8 \\
\hline Price per Unit $(P)$ & 3 & $7 / 3$ & 2 & $9 / 5$ & $5 / 3$ \\
\hline
\end{tabular}

Write a rational function statement for the price $(\mathbf{P})$ per unit if $x$ number of items are bought.

Step 1 ：The problem is asking for a rational function that describes the relationship between the number of items bought (x) and the price per unit (P). A rational function is a function that is the ratio of two polynomials.

Step 2 ：To find this function, we can use the method of interpolation, which involves finding a polynomial that passes through a given set of points. In this case, the points are the pairs of x and P values given in the table.

Step 3 ：We can use the Lagrange interpolation formula to find this polynomial. The formula is: \(P(x) = \Sigma (y_i * L_i(x))\) where \(y_i\) are the y values (in this case, the price per unit), \(L_i(x)\) are the Lagrange basis polynomials, and the sum is taken over all given points.

Step 4 ：The Lagrange basis polynomials are given by: \(L_i(x) = \Pi ((x - x_j) / (x_i - x_j))\) where the product is taken over all \(j \neq i\).

Step 5 ：Using these formulas, we can calculate the polynomial function that describes the relationship between the number of items bought (x) and the price per unit (P). This function is: \(P(x) = 0.00555555555555554x^4 - 0.155555555555557x^3 + 1.66111111111111x^2 - 8.17777777777775x + 17.6666666666667\)

Step 6 ：This function should be able to predict the price per unit for any given number of items bought. However, it's important to note that this function is only an approximation, and it may not be accurate for values of x that are outside the range of the given data.

Step 7 ：Final Answer: The rational function statement for the price (P) per unit if x number of items are bought is \(\boxed{P(x) = 0.00555555555555554x^4 - 0.155555555555557x^3 + 1.66111111111111x^2 - 8.17777777777775x + 17.6666666666667}\).