Đáp án:

$a)B(7-4\sqrt{3})=-\dfrac{2\sqrt{3}}{3}\\ b)P=\dfrac{\sqrt{x}+2}{\sqrt{x}+1}\\ c) x=4\\ d)x=5$

Giải thích các bước giải:

$a)B(7-4\sqrt{3})\\ =\dfrac{2}{\sqrt{7-4\sqrt{3}}-2}\\ =\dfrac{2}{\sqrt{4-2.2\sqrt{3}+3}-2}\\ =\dfrac{2}{\sqrt{(2-\sqrt{3})^2}-2}\\ =\dfrac{2}{(2-\sqrt{3})-2}\\ =\dfrac{2}{-\sqrt{3}}\\ =-\dfrac{2\sqrt{3}}{3}\\ b)A=\dfrac{\sqrt{x}}{x-4}+\dfrac{1}{\sqrt{x}-2}\\ =\dfrac{\sqrt{x}}{(\sqrt{x}-2)(\sqrt{x}+2)}+\dfrac{1}{\sqrt{x}-2}\\ =\dfrac{\sqrt{x}}{(\sqrt{x}-2)(\sqrt{x}+2)}+\dfrac{\sqrt{x}+2}{(\sqrt{x}-2)(\sqrt{x}+2)}\\ =\dfrac{\sqrt{x}+\sqrt{x}+2}{(\sqrt{x}-2)(\sqrt{x}+2)}\\ =\dfrac{2\sqrt{x}+2}{(\sqrt{x}-2)(\sqrt{x}+2)}\\ P=\dfrac{B}{A}\\ =\dfrac{\dfrac{2}{\sqrt{x}-2}}{\dfrac{2\sqrt{x}+2}{(\sqrt{x}-2)(\sqrt{x}+2)}}\\ =\dfrac{2(\sqrt{x}-2)(\sqrt{x}+2)}{2(\sqrt{x}+1)(\sqrt{x}-2)}\\ =\dfrac{\sqrt{x}+2}{\sqrt{x}+1}\\ c)P=\dfrac{4}{3} \\ \Leftrightarrow \dfrac{\sqrt{x}+2}{\sqrt{x}+1}=\dfrac{4}{3} \\ \Leftrightarrow \dfrac{\sqrt{x}+2}{\sqrt{x}+1}-\dfrac{4}{3}=0\\ \Leftrightarrow \dfrac{3(\sqrt{x}+2)-4(\sqrt{x}+1)}{3(\sqrt{x}+1)}=0\\ \Leftrightarrow \dfrac{2-\sqrt{x}}{3(\sqrt{x}+1)}=0\\ \Leftrightarrow 2-\sqrt{x}=0\\ \Leftrightarrow \sqrt{x}=2\\ \Leftrightarrow x=4\\ d)(\sqrt{x}+1)P-\sqrt{x}-4\sqrt{x-1}+26=-6x+10\sqrt{5x}\\ \Leftrightarrow (\sqrt{x}+1)\dfrac{\sqrt{x}+2}{\sqrt{x}+1}-\sqrt{x}-4\sqrt{x-1}+26=-6x+10\sqrt{5x}\\ \Leftrightarrow \sqrt{x}+2-\sqrt{x}-4\sqrt{x-1}+26=-6x+10\sqrt{5x}\\ \Leftrightarrow -4\sqrt{x-1}+28=-6x+10\sqrt{5x}\\ \Leftrightarrow -2\sqrt{x-1}+14=-3x+5\sqrt{5x}\\ \Leftrightarrow 14+3x=5\sqrt{5x}+2\sqrt{x-1}\\ \Rightarrow (14+3x)^2=(5\sqrt{5x}+2\sqrt{x-1})^2\\ \Leftrightarrow 196+84x+9x^2=125x+20\sqrt{5x(x-1)}+4(x-1)\\ \Leftrightarrow 9x^2-45x-20\sqrt{5x(x-1)}+200=0\\ \Leftrightarrow 9x^2-45x+200=20\sqrt{5x(x-1)}\\ \Rightarrow (9x^2-45x+200)^2=(20\sqrt{5x(x-1)})^2\\ \Leftrightarrow (9x^2-45x+200)(9x^2-45x+200)=2000x(x-1)\\ \Leftrightarrow 81x^4−810x^3+5625x^2−18000x+40000=2000x^2-2000x\\ \Leftrightarrow 81x^4−810x^3+3625x^2−16000x+40000=0\\ \Leftrightarrow 81x^4−405x^3-405x^3+2025x^2+1600x^2−8000x−8000x+40000=0\\ \Leftrightarrow 81x^3(x-5)-405x^2(x-5)+1600x(x-5)−8000(x-5)=0\\ \Leftrightarrow (x-5)(81x^3-405x^2+1600x−8000)=0\\ \Leftrightarrow  \left[\begin{array}{l} x-5=0\\81x^3-405x^2+1600x−8000 =0\end{array} \right.\\ \Leftrightarrow x=5$