Bài 7:
1: \(P=\frac{2\sqrt{a}}{\sqrt{a}+3}+\frac{\sqrt{a}+1}{\sqrt{a}-3}+\frac{3+7\sqrt{a}}{9-a}\)
\(=\frac{2\sqrt{a}\left(\sqrt{a}-3\right)+\left(\sqrt{a}+1\right)\left(\sqrt{a}+3\right)-3-7\sqrt{a}}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-3\right)}\)
\(=\frac{2a-6\sqrt{a}+a+4\sqrt{a}+3-3-7\sqrt{a}}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-3\right)}=\frac{3a-9\sqrt{a}}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-3\right)}=\frac{3\sqrt{a}}{\sqrt{a}+3}\)
2: P<1
=>P-1<0
=>\(\frac{3\sqrt{a}-\sqrt{a}-3}{\sqrt{a}+3}<0\)
=>\(2\sqrt{a}-3<0\)
=>\(2\sqrt{a}<3\)
=>\(\sqrt{a}<\frac32\)
=>0<=a<9/4
Bài 7:
1: \(A=\frac{5\sqrt{x}}{\sqrt{x}-2}+\frac{\sqrt{x}-1}{\sqrt{x}+2}-\frac{5x+2}{x-4}\)
\(=\frac{5\sqrt{x}\left(\sqrt{x}+2\right)+\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)-5x-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\frac{5x+10\sqrt{x}+x-3\sqrt{x}+2-5x-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\frac{x+7\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(P=A\cdot B\)
\(=\frac{\sqrt{x}\left(\sqrt{x}+7\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\frac{x-4}{x+2\sqrt{x}}=\frac{\sqrt{x}\left(\sqrt{x}+7\right)}{\sqrt{x}\left(\sqrt{x}+2\right)}=\frac{\sqrt{x}+7}{\sqrt{x}+2}\)
2: P>2
=>P-2>0
=>\(\frac{\sqrt{x}+7-2\sqrt{x}-4}{\sqrt{x}+2}>0\)
=>\(-\sqrt{x}+3>0\)
=>\(-\sqrt{x}>-3\)
=>\(\sqrt{x}<3\)
=>0<x<9
Kết hợp ĐKXĐ, ta được: 0<x<9 và x<>4
