GIve :

\(A=\dfrac{\sqrt{x}+4}{\sqrt{x}+2}\)

\(B=\left(\dfrac{\sqrt{x}}{\sqrt{x}+4}+\dfrac{4}{\sqrt{x}-4}\right):\dfrac{x+16}{\sqrt{x}+2}\)

a) Shorten B ?

b) Find x interger so \(B\left(A-1\right)\) is also interger.

Give :

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

a) Shorten P ?

b) With which x we have \(\dfrac{1}{P}-\dfrac{\sqrt{x}+1}{8}\ge1\) ?