Question

Tính P = A : B biết B=\(\dfrac{x}{x-4}-\dfrac{\sqrt{x}+3}{x+\sqrt{x}-6}\), A=\(\dfrac{\sqrt{x}-1}{\sqrt{x}+2}\)

Answer 1

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

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

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

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