Answer:
[tex]\dfrac{\sqrt{x+3}+\sqrt{x}}{3}[/tex]
Step-by-step explanation:
given expression,
[tex]\dfrac{1}{\sqrt{x+3}-\sqrt{x}}[/tex]
on rationalizing
multiplying both numerator and denominator by [tex]\sqrt{x+3}+\sqrt{x}[/tex]
[tex]\dfrac{1}{\sqrt{x+3}-\sqrt{x}}\times \dfrac{\sqrt{x+3}+\sqrt{x}}{\sqrt{x+3}+\sqrt{x}}[/tex]
[tex]\dfrac{\sqrt{x+3}+\sqrt{x}}{(\sqrt{x+3})^2-(\sqrt{x})^2}[/tex]
[tex]\dfrac{\sqrt{x+3}+\sqrt{x}}{(x+3)-(x)}[/tex]
[tex]\dfrac{\sqrt{x+3}+\sqrt{x}}{3}[/tex]
