Question

Cho biểu thức: B =\(\dfrac{\sqrt{x}+2}{\sqrt{x}+1}-\dfrac{3}{\left(\sqrt{x}+1\right)\left(2-\sqrt{x}\right)}\) với x ≥ 0; x ≠ 4 

Chứng minh B = \(\dfrac{\sqrt{x}-1}{\sqrt{x}-2}\)

 

Answer 1

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

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

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

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