Question

Can someone explain this to me.

Answer 1

Answer:

option D

$3*(\sqrt{x}+\sqrt{x-3})$

Step-by-step explanation:

Given in the question an expression,

$\frac{9}{\sqrt{x} -\sqrt{x-3}}$

Step 1

Divide and multiple by $\sqrt{x}+\sqrt{x-3}$ to remove radical sign from denominator.

$\frac{9}{\sqrt{x} -\sqrt{x-3}}*\frac{\sqrt{x} +\sqrt{x-3}}{\sqrt{x} +\sqrt{x-3}}$

Step 2

Apply a² - b² = (a+b)(a-b)

$\frac{9*\sqrt{x}+\sqrt{x-3}}{\sqrt{x^{2}}-\sqrt{(x-3)^{2}}}}$

Step 3

$\frac{9*\sqrt{x}+\sqrt{x-3}}{x-x+3}$

Step 4

$\frac{9*\sqrt{x}+\sqrt{x-3}}{3}$

Step 5

$3*(\sqrt{x}+\sqrt{x-3})$