Question

Cho biểu thức

P=\(\frac{\sqrt{x}+1}{\sqrt{x}+3}+\frac{\sqrt{x}-2}{\sqrt{x}-1}-\frac{2x-10}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)

Rút gọn P,tìm x để P>0

Answer 1

đk: \(x\ge0\)và      \(x\ne1\)

\(\Leftrightarrow P=\frac{x-1+\left(\sqrt{x}-2\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x-1}\right)}-\frac{2x-10}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)

\(\Leftrightarrow P=\frac{x-1+x+\sqrt{x}-6-2x+10}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)

\(\Leftrightarrow P=\frac{\sqrt{x}+3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}=\frac{1}{\sqrt{x}-1}\)

để P > 0

\(\Leftrightarrow1>\sqrt{x}-1\)

\(\Leftrightarrow-\sqrt{x}>-2\)

\(\Leftrightarrow\sqrt{x}< 2\)

\(\Leftrightarrow x< 4\)

có sai xót mong m.n bỏ qa cho ♥