1) Cho biểu thức :
\(P=\left(\dfrac{1}{\sqrt{a}-3}+\dfrac{1}{\sqrt{a}+3}\right).\left(1-\dfrac{3}{\sqrt{a}}\right)\) ( với \(a>0;a\ne9\))
a) Rút gọn P
b) Tính giá trị của a để \(P>\dfrac{1}{2}\)
2) Cho biểu thức :
\(C=\dfrac{2\sqrt{a}}{\sqrt{a}+3}+\dfrac{\sqrt{a}+1}{\sqrt{a}-3}+\dfrac{3+7\sqrt{a}}{9-a}\) (với \(a\ge0;a\ne9\) )
a) Rút gọn C
b) Tìm a để \(C< 1\)
1)
a. \(P=\left(\dfrac{1}{\sqrt{a}-3}+\dfrac{1}{\sqrt{a}+3}\right)\left(1-\dfrac{3}{\sqrt{a}}\right)\)
\(\Leftrightarrow\left(\dfrac{\left(\sqrt{a}+3\right)}{\left(\sqrt{a}-3\right)\left(\sqrt{a}+3\right)}+\dfrac{\left(\sqrt{a}-3\right)}{\left(\sqrt{a}-3\right)\left(\sqrt{a}+3\right)}\right)\left(\dfrac{\sqrt{a}}{\sqrt{a}}-\dfrac{3}{\sqrt{a}}\right)\)\(\Leftrightarrow\dfrac{\sqrt{a}+3+\sqrt{a}-3}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-3\right)}.\dfrac{\sqrt{a}-3}{\sqrt{a}}\)
\(\Leftrightarrow\dfrac{2\sqrt{a}\left(\sqrt{a}-3\right)}{\sqrt{a}\left(\sqrt{a-3}\right)\left(\sqrt{a}+3\right)}\)
\(\Leftrightarrow\dfrac{2}{\sqrt{a}+3}\)
b.
