1: \(P=\dfrac{x-\sqrt{x}+\sqrt{x}-3-\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{x-\sqrt{x}-6}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\dfrac{\sqrt{x}+2}{\sqrt{x}+3}\)
2:
a: Khi x=4 thì \(P=\dfrac{2+2}{2+3}=\dfrac{4}{5}\)
b: Khi x=7+4căn3 thì \(P=\dfrac{2+\sqrt{3}+2}{2+\sqrt{3}+3}=\dfrac{4+\sqrt{3}}{5+\sqrt{3}}=\dfrac{17+\sqrt{3}}{22}\)
c: \(x=\dfrac{\sqrt{2}+1-\sqrt{2}+1}{\left(2-1\right)}=2\)
Khi x=2 thì \(P=\dfrac{2+\sqrt{2}}{3+\sqrt{2}}=\dfrac{4+\sqrt{2}}{7}\)
3: a: P=7/9
=>\(\dfrac{\sqrt{x}+2}{\sqrt{x}+3}=\dfrac{7}{9}\)
=>\(9\sqrt{x}+18=7\sqrt{x}+21\)
=>2*căn x=3
=>căn x=3/2
=>x=9/4
b: \(P=\sqrt{x}-\dfrac{1}{4}=\dfrac{4\sqrt{x}-1}{4}\)
=>\(\dfrac{\sqrt{x}+2}{\sqrt{x}+3}=\dfrac{4\sqrt{x}-1}{4}\)
=>\(\left(4\sqrt{x}-1\right)\left(\sqrt{x}+3\right)=4\left(\sqrt{x}+2\right)\)
=>\(4x+12\sqrt{x}-\sqrt{x}-3-4\sqrt{x}-8=0\)
=>\(4x+7\sqrt{x}-11=0\)
=>(4căn x+11)(căn x-1)=0
=>x=1(nhận)
