5. a. Given that
$$\frac { x ^ { 2 } - 1 } { x + 3 } \equiv x + P + \frac { Q } { x + 3 }$$
find the value of the constant \(P\) and show that \(Q = 8\)
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\includegraphics[alt={},max width=\textwidth]{cb92f7b6-2ba5-4703-9595-9ba8570fc52b-07_1082_1271_1363_415}
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\caption{Figure 3}
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The curve \(C\) has equation \(y = \mathrm { g } ( x )\), where
$$\mathrm { g } ( x ) = \frac { x ^ { 2 } - 1 } { x + 3 } \quad x > - 3$$
Figure 3 shows a sketch of the curve \(C\).
The region \(R\), shown shaded in Figure 4, is bounded by \(C\), the \(x\)-axis and the line with equation \(x = 5\).
b. Find the exact area of \(R\), writing your answer in the form \(a \ln 2\), where \(a\) is constant to be found.
(4)