Answer:
The solved expression is [tex]\frac{3}{\sqrt{3}-11}=-\frac{3\sqrt{3}+33}{118}[/tex]
Step-by-step explanation:
Given expression is [tex]\frac{3}{\sqrt{3}-11}[/tex]
To rationalize the given expression as below :
[tex]\frac{3}{\sqrt{3}-11}[/tex]
Multiply and divide the conjugate of denominator [tex]\sqrt{3}-11[/tex] is [tex]\sqrt{3}+11[/tex] we get
[tex]=\frac{\frac{3}{\sqrt{3}-11}\times \sqrt{3}+11}{\sqrt{3}+11}[/tex]
[tex]=\frac{3(\sqrt{3}+11)}{(\sqrt{3}-11)(\sqrt{3}+11)}[/tex]
[tex]=\frac{3(\sqrt{3}+3(11)}{(\sqrt{3})^2-11^2}[/tex] ( using the formula [tex](a-b)(a+b)=a^2-b^2[/tex] )
[tex]=\frac{3\sqrt{3}+33}{3-121}[/tex]
[tex]=\frac{3\sqrt{3}+33}{-118}[/tex]
[tex]=-\frac{3\sqrt{3}+33}{118}[/tex]
Therefore the solved expression is [tex]-\frac{3\sqrt{3}+33}{118}[/tex]
Therefore the given expression is [tex]\frac{3}{\sqrt{3}-11}=-\frac{3\sqrt{3}+33}{118}[/tex].
