Question

Answer 1

a: ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x\ne1\end{matrix}\right.\)

\(P=\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{1}{x-1}\right):\left(2-\dfrac{\sqrt{x}-4}{\sqrt{x}-1}\right)\)

\(=\dfrac{1+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}:\dfrac{2\left(\sqrt{x}-1\right)-\sqrt{x}+4}{\left(\sqrt{x}-1\right)}\)

\(=\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\cdot\dfrac{\sqrt{x}-1}{\sqrt{x}+2}=\dfrac{1}{\sqrt{x}+1}\)

b: \(\sqrt{x}+1>=1\forall x\) thỏa mãn ĐKXĐ

=>P=\(\dfrac{1}{\sqrt{x}+1}< =1\forall x\) thỏa mãn ĐKXĐ

Dấu '=' xảy ra khi x=0