Answer:
OPTION C
Step-by-step explanation:
We are given the expression: [tex]$ \frac{\sqrt{x}}{\sqrt{x} + \sqrt{5}} $[/tex]
We multiply and divide the expression by the conjugate of the denominator.
So, we will get:
[tex]$ \frac{\sqrt{x}}{\sqrt{x} + \sqrt{5}} = \frac{\sqrt{x}.(\sqrt{x} - \sqrt{5})}{\sqrt{x} + \sqrt{5} . \sqrt{x} - \sqrt{5}} $[/tex]
[tex]$ \sqrt{x} + \sqrt{5}. \sqrt{x} - \sqrt{5} = x - 5 $[/tex] since it is of the form (a + b)(a - b) which is equal to [tex]$ a^2 - b ^2 $[/tex].
[tex]$ \therefore \frac{\sqrt{x}{(\sqrt{x} - \sqrt{5})}}{x - 5} = \frac{\sqrt{x}.\sqrt{x}- \sqrt{5x}}{x - 5}$[/tex]
[tex]$ = \frac{x - \sqrt{5x}}{x - 5} $[/tex]
Hence, OPTION C is the answer.
