1) Thay x=4 (t/m) vào A:
A= \(\dfrac{\sqrt{4}+1}{\sqrt{4}+2}=\dfrac{2+1}{2+2}=\dfrac{3}{4}\)
Vậy A=\(\dfrac{3}{4}\)khi x =4
2) \(B=\dfrac{3}{\sqrt{x}-1}-\dfrac{\sqrt{x}+5}{x-1}\left(x\ge0;x\ne1\right)\\ B=\dfrac{3\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\dfrac{\sqrt{x}+5}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\\ B=\dfrac{3\sqrt{x}+3-\sqrt{x}-5}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\\ B=\dfrac{2\sqrt{x}-2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\\ B=\dfrac{2\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}=\dfrac{2}{\sqrt{x}+1}\)
3)\(P=2AB+\sqrt{x}\\ P=2.\dfrac{\sqrt{x}+1}{\sqrt{x}+2}.\dfrac{2}{\sqrt{x}+1}+\sqrt{x}\left(x\ge0;x\ne1\right)\\ P=\dfrac{4+x+2\sqrt{x}}{\sqrt{x}+2}\\ P=\dfrac{\left(\sqrt{x}+2\right)^2}{\sqrt{x}+2}=\sqrt{x}+2\)
