Question

Answer 1

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

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

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

b: \(Q=P-\sqrt{x}=\dfrac{x+2-x+\sqrt{x}}{\sqrt{x}-1}=\dfrac{\sqrt{x}+2}{\sqrt{x}-1}=1+\dfrac{3}{\sqrt{x}-1}\)

Q nguyên

=>căn x-1 thuộc {1;-1;3;-3}

=>x thuộc {4;0;16}