Ta có:\(P=\dfrac{14-x}{4+x}\)
\(P=\dfrac{14+x-2x}{4+x}\)
\(P=\dfrac{4+x-2x-8+18}{4+x}\)
\(P=\dfrac{4+x-\left(2x+8\right)+18}{4+x}\)
\(P=\dfrac{4+x-2\left(x+4\right)+18}{4+x}\)
\(P=\dfrac{\left(4+x\right)\left(1-2\right)+18}{4+x}\)
\(P=\dfrac{-\left(4+x\right)+18}{4+x}\)
\(P=-1+\dfrac{18}{4+x}\)
\(P=-1+\dfrac{18}{4+x}\le-1+18\left(x\in Z\right)\)
\(P\le17\)
\(\Rightarrow\)GTLN của P là 17 khi x=-3
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