hẹn ngày mai, giao hàng hôm nay, không lỡ hẹn nhé
a) ĐK: \(x\ne1\)
\(P=\left(\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}-\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right):\left(\dfrac{\sqrt{x}-1-\sqrt{x}-1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right)\)
\(=\left(\dfrac{\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)}-\dfrac{\sqrt{x}}{\left(\sqrt{x}-1\right)}\right)\cdot\left(\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{-2}\right)\)
\(=\dfrac{1}{\sqrt{x}-1}\cdot\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{-2}\) \(=\dfrac{-\sqrt{x}-1}{2}\)
b) P=4
\(P=-4\Leftrightarrow\dfrac{-\sqrt{x}-1}{2}=-4\Leftrightarrow-\sqrt{x}-1=-8\Leftrightarrow\sqrt{x}=9\Leftrightarrow x=81\left(N\right)\)
c) \(x=8-2\sqrt{15}\Rightarrow\sqrt{x}=\sqrt{5}-\sqrt{3}\)
Thay \(\sqrt{x}=\sqrt{5}-\sqrt{3}\) vào P, ta được:
\(P=\dfrac{-\sqrt{5}+\sqrt{3}-1}{2}\)
KL: a) ĐK: \(x\ne1\)
\(P=\dfrac{-\sqrt{x}-1}{2}\)
b) x= 81
c) \(P=\dfrac{-\sqrt{5}+\sqrt{3}-1}{2}\)