Question

Answer 1

a: \(B=\dfrac{\sqrt{x}-1}{\sqrt{x}-3}-\dfrac{7\sqrt{x}-9}{x-9}\)

\(=\dfrac{\sqrt{x}-1}{\sqrt{x}-3}-\dfrac{7\sqrt{x}-9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)

\(=\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)-7\sqrt{x}+9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)

\(=\dfrac{x+2\sqrt{x}-3-7\sqrt{x}+9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\dfrac{x-5\sqrt{x}+6}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)

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

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

Thay x=2 vào A, ta được:

\(A=\dfrac{\sqrt{2}-2}{\sqrt{2}}=1-\sqrt{2}\)

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

=>\(m=P=\dfrac{\sqrt{x}+3}{\sqrt{x}}\)