Đáp án:
\(Min = - \dfrac{7}{9}\)
Giải thích các bước giải:
\(\begin{array}{l}
P = \dfrac{{\left| {x + 5} \right| - 7}}{{\left| {x + 5} \right| + 9}} = \dfrac{{\left| {x + 5} \right| + 9 - 16}}{{\left| {x + 5} \right| + 9}}\\
= 1 - \dfrac{{16}}{{\left| {x + 5} \right| + 9}}\\
Do:\left| {x + 5} \right| \ge 0\forall x\\
\to \left| {x + 5} \right| + 9 \ge 9\\
\to \dfrac{{16}}{{\left| {x + 5} \right| + 9}} \le \dfrac{{16}}{9}\\
\to - \dfrac{{16}}{{\left| {x + 5} \right| + 9}} \ge - \dfrac{{16}}{9}\\
\to 1 - \dfrac{{16}}{{\left| {x + 5} \right| + 9}} \ge - \dfrac{7}{9}\\
\to Min = - \dfrac{7}{9}\\
\Leftrightarrow x + 5 = 0\\
\to x = - 5
\end{array}\)