\(a,P=B:A\)
\(=\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-3}\right):\left(\dfrac{2}{\sqrt{x}-3}+\dfrac{1}{\sqrt{x}+3}\right)\left(ĐKXĐ:x\ge0;x\ne9\right)\)
\(=\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-3}\right):\left[\dfrac{2\left(\sqrt{x}+3\right)+\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right]\)
\(=\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-3}\right):\left[\dfrac{3\sqrt{x}+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right]\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}-3}\cdot\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}{3\left(\sqrt{x}+1\right)}\)
\(=\dfrac{\sqrt{x}+3}{3}\)
\(b,\) Để \(P=\dfrac{\sqrt{x}+3}{3}\) có giá trị nguyên
thì \(\sqrt{x}+3⋮3\)
\(\Leftrightarrow\sqrt{x}+3\in B\left(3\right)\)
\(\Leftrightarrow\sqrt{x}\in B\left(3\right)\)
Kết hợp với điều kiện, ta được:
\(P\) nguyên khi \(x=m^2\left(m\in Z;m⋮3;m\ne3\right)\)
#Toru
a:
ĐKXĐ: x>=0; x<>9
\(A=\dfrac{2\sqrt{x}+6+\sqrt{x}-3}{\left(x-9\right)}=\dfrac{3\sqrt{x}+3}{x-9}\)
\(P=B:A=\dfrac{\sqrt{x}+1}{\sqrt{x}-3}\cdot\dfrac{x-9}{3\left(\sqrt{x}+1\right)}=\dfrac{\sqrt{x}+3}{3}\)
b: P nguyên khi \(\sqrt{x}+3⋮3\)
=>\(\sqrt{x}\in B\left(3\right)\)
=>\(x=k^2\left(k\in Z;k⋮3\right)\)
