Answer:
option D
[tex]3*(\sqrt{x}+\sqrt{x-3})[/tex]
Step-by-step explanation:
Given in the question an expression,
[tex]\frac{9}{\sqrt{x} -\sqrt{x-3}}[/tex]
Step 1
Divide and multiple by [tex]\sqrt{x}+\sqrt{x-3}[/tex] to remove radical sign from denominator.
[tex]\frac{9}{\sqrt{x} -\sqrt{x-3}}*\frac{\sqrt{x} +\sqrt{x-3}}{\sqrt{x} +\sqrt{x-3}}[/tex]
Step 2
Apply a² - b² = (a+b)(a-b)
[tex]\frac{9*\sqrt{x}+\sqrt{x-3}}{\sqrt{x^{2}}-\sqrt{(x-3)^{2}}}}[/tex]
Step 3
[tex]\frac{9*\sqrt{x}+\sqrt{x-3}}{x-x+3}[/tex]
Step 4
[tex]\frac{9*\sqrt{x}+\sqrt{x-3}}{3}[/tex]
Step 5
[tex]3*(\sqrt{x}+\sqrt{x-3})[/tex]
