a) \(ĐKXĐ:x\ne-3;x\ne2\)
b) \(P=\frac{\left(x+2\right)\left(x-2\right)}{\left(x+3\right)\left(x-2\right)}-\frac{5}{\left(x-2\right)\left(x+3\right)}-\frac{x+3}{\left(x-2\right)\left(x+3\right)}\)
\(P=\frac{x^2-4-5-x-3}{\left(x+3\right)\left(x-2\right)}\)
\(P=\frac{x^2-x-12}{\left(x+3\right)\left(x-2\right)}\)
\(P=\frac{\left(x+3\right)\left(x-4\right)}{\left(x+3\right)\left(x-2\right)}\)
vậy \(P=\frac{x-4}{x-2}\)
\(P=\frac{-3}{4}\) \(\Leftrightarrow\frac{x-4}{x-2}=\frac{-3}{4}\)
\(\Leftrightarrow4\left(x-4\right)=-3.\left(x-2\right)\)
\(\Leftrightarrow4x-16=-3x+6\)
\(\Leftrightarrow7x=22\)
\(\Leftrightarrow x=\frac{22}{7}\)
c) \(P\in Z\Leftrightarrow\frac{x-4}{x-2}\in Z\)
\(\frac{x-2-6}{x-2}=1-\frac{6}{x-2}\in Z\)
mà \(1\in Z\Rightarrow\left(x-2\right)\inƯ\left(6\right)\in\left(\pm1;\pm2;\pm3;\pm6\right)\)
mà theo ĐKXĐ: \(\Rightarrow\in\left(\pm1;-2;3;\pm6\right)\)
thay mấy cái kia vào rồi tìm \(x\)
d) \(x^2-9=0\Rightarrow x^2=9\Rightarrow x=\pm3\)
khi \(x=3\Rightarrow P=\frac{3-4}{3-2}=-1\)
khi \(x=-3\Rightarrow P=\frac{-3-4}{-3-2}=\frac{-7}{-5}=\frac{7}{5}\)
