Respuesta :

luisejr77

Answer: OPTION D

Step-by-step explanation:

You need to remember this property:

[tex]\frac{\sqrt{x} }{\sqrt{y} }=\sqrt{\frac{x}{y} }[/tex]

And remember that:

[tex]\frac{a}{a}=1[/tex]

Then, the first step is rewrite the expression:

[tex]\frac{\sqrt{30(x-1)} }{\sqrt{5(x-1)^2}}[/tex] [tex]=\sqrt{\frac{30(x-1)}{5(x-1)^2}} }[/tex]

Now, to find the corresponding equivalent expression, you need to simplify the expression.

Therefore, the equivalent expression is the following:

[tex]\sqrt{\frac{6}{(x-1)}} }[/tex]

Finally, you can observe that this matches with the option D.

Answer:

Choice D

Step-by-step explanation:

The division of the two radicals can be re-written in the following format;

[tex]\frac{\sqrt{30(x-1)} }{\sqrt{5(x-1)^{2} } }[/tex]

Using the properties of radicals division, the expression can further be written as;

[tex]\sqrt{\frac{30(x-1)}{5(x-1)^{2} } }[/tex]

We simplify the terms under the radical sign to obtain;

[tex]\sqrt{\frac{6}{x-1} }[/tex]

Choice D is thus the correct solution