Bài 1:
1) \(P=\dfrac{\sqrt{x}-1}{3\sqrt{x}-1}-\dfrac{1}{3\sqrt{x}+1}+\dfrac{4\sqrt{x}}{9x-1}\) (ĐK: \(x\ge0;x\ne\dfrac{1}{9}\))
\(P=\dfrac{\sqrt{x}-1}{3\sqrt{x}-1}-\dfrac{1}{3\sqrt{x}+1}+\dfrac{4\sqrt{x}}{\left(3\sqrt{x}+1\right)\left(3\sqrt{x}-1\right)}\)
\(P=\dfrac{\left(\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}{\left(3\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}-\dfrac{3\sqrt{x}-1}{\left(3\sqrt{x}+1\right)\left(3\sqrt{x}-1\right)}+\dfrac{4\sqrt{x}}{\left(3\sqrt{x}+1\right)\left(3\sqrt{x}-1\right)}\)
\(P=\dfrac{3x+\sqrt{x}-3\sqrt{x}-1-3\sqrt{x}+1+4\sqrt{x}}{\left(3\sqrt{x}+1\right)\left(3\sqrt{x}-1\right)}\)
\(P=\dfrac{3x-\sqrt{x}}{\left(3\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}\)
\(P=\dfrac{\sqrt{x}\left(3\sqrt{x}-1\right)}{\left(3\sqrt{x}+1\right)\left(3\sqrt{x}-1\right)}\)
\(P=\dfrac{\sqrt{x}}{3\sqrt{x}+1}\)
2) \(P=\dfrac{1}{4}\) khi và chỉ khi:
\(\dfrac{\sqrt{x}}{3\sqrt{x}+1}=\dfrac{1}{4}\)
\(\Leftrightarrow4\sqrt{x}=3\sqrt{x}+1\)
\(\Leftrightarrow\sqrt{x}=1\)
\(\Leftrightarrow x=1\)
