\(a,P=\left(\dfrac{2}{x+4}+\dfrac{x+20}{x^2-16}\right).\dfrac{x-4}{x+5}=\dfrac{2\left(x-4\right)+x+20}{\left(x-4\right)\left(x+4\right)}.\dfrac{x-4}{x+5}=\dfrac{2x-8+x+20}{\left(x+4\right)\left(x+5\right)}=\dfrac{3x+12}{\left(x+4\right)\left(x+5\right)}=\dfrac{3\left(x+4\right)}{\left(x+4\right)\left(x+5\right)}=\dfrac{3}{x+5}\)
\(x^2+4x=0\\ \Rightarrow x\left(x+4\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=-4\end{matrix}\right.\)
Thay x=0 vào P⇒\(P=\dfrac{3}{x+5}=\dfrac{3}{0+5}=\dfrac{3}{5}\)
Thay x=-4 vào P⇒\(P=\dfrac{3}{x+5}=\dfrac{3}{-4+5}=\dfrac{3}{1}=3\)
c, Để P nguyên thì \(\dfrac{3}{x+5}\in Z\Rightarrow x+5\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\Rightarrow x\in\left\{-8;-6;-4;-2\right\}\)
a: \(P=\dfrac{2x-8+x+20}{\left(x+4\right)\left(x-4\right)}\cdot\dfrac{x-4}{x+5}=\dfrac{3}{x+5}\)
a) \(P=\left(\dfrac{2}{x+4}+\dfrac{x+20}{x^2-16}\right).\dfrac{x-4}{x+5}\left(x\ne-5;x\ne-4;x\ne4\right).\)
\(P=\dfrac{2\left(x-4\right)+x+20}{\left(x-4\right)\left(x+4\right)}.\dfrac{x-4}{x+5}=\dfrac{2x-8+x+20}{x+4}.\dfrac{1}{x+5}.\)
\(P=\dfrac{3x+12}{\left(x+4\right)\left(x+5\right)}=\dfrac{3\left(x+4\right)}{\left(x+4\right)\left(x+5\right)}=\dfrac{3}{x+5}\left(đpcm\right).\)
b) \(x^2+4x=0.\Leftrightarrow x\left(x+4\right)=0.\Leftrightarrow\left[{}\begin{matrix}x=0\left(TM\right).\\x=-4\left(koTM\right).\end{matrix}\right.\)
Thay \(\text{x = 0}\) vào biểu thức P: \(\dfrac{3}{0+5}=\dfrac{3}{5}.\)
