a) \(P=\left(\dfrac{3}{\sqrt{x}-5}-\dfrac{2}{\sqrt{x}+1}\right):\dfrac{\sqrt{x}+13}{x+\sqrt{x}}\)
\(P=\left[\dfrac{3\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+1\right)}-\dfrac{2\left(\sqrt{x}-5\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+1\right)}\right]\cdot\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}+13}\)
\(P=\dfrac{3\sqrt{x}+3-2\sqrt{x}+10}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+1\right)}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}+13}\)
\(P=\dfrac{\sqrt{x}+13}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+1\right)}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}+13}\)
\(P=\dfrac{\sqrt{x}}{\sqrt{x}-5}\)
b) \(P=6\) khi:
\(\dfrac{\sqrt{x}}{\sqrt{x}-5}=6\)
\(\Leftrightarrow\sqrt{x}=6\left(\sqrt{x}-5\right)\)
\(\Leftrightarrow\sqrt{x}=6\sqrt{x}-30\)
\(\Leftrightarrow5\sqrt{x}=30\)
\(\Leftrightarrow\sqrt{x}=6\)
\(\Leftrightarrow x=36\left(tm\right)\)
c) \(P< 0\) khi:
\(\dfrac{\sqrt{x}}{\sqrt{x}-5}< 0\)
\(\Leftrightarrow\sqrt{x}-5< 0\)
\(\Leftrightarrow\sqrt{x}< 5\)
\(\Leftrightarrow x< 25\)
Kết hợp với ĐK:
\(0< x< 25\)
a: \(P=\dfrac{3\sqrt{x}+3-2\sqrt{x}+10}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+1\right)}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}+13}\)
\(=\dfrac{\sqrt{x}+13}{\sqrt{x}-5}\cdot\dfrac{\sqrt{x}}{\sqrt{x}+13}=\dfrac{\sqrt{x}}{\sqrt{x}-5}\)
b: P=6
=>căn x=6căn x-30
=>-5căn x=-30
=>căn x=6
=>x=36(nhận)
c: P<0
=>căn x-5<0
=>0<x<25
giúp e vs ạ ;-;
giúp e vs ạ :<