Question 28: \(\text { Find } x \text { in an integer such that the expression } A=\frac{14-x}{4-x} \text { reaches the maximum value. }\)

\(\begin{aligned} &\mathrm{A}=\frac{(4-x)+10}{4-x}=1+\frac{10}{4-x} \\ &\text { To } \mathrm{A}_{\max } \Leftrightarrow \frac{10}{4-x} \max \\ &\text { TH1: } 4-\mathrm{x}<0 \text { then } \frac {10}{4-x}<0 \text { (type) } \\ &\text { TH2: } 4-\mathrm{x}>0 \Leftrightarrow \mathrm{x}<4 \text { then } \ frac{10}{4-x} \max \Leftrightarrow(4-\mathrm{x})_ \min \Leftrightarrow \mathrm{x}_ \max \Leftrightarrow \mathrm{x}=3 \end{aligned}\ )