Question

Which choice is equivalent to the quotient shown here for acceptable values of x?

Answer 1

Answer:

Choice D

Step-by-step explanation:

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

$\frac{\sqrt{30(x-1)} }{\sqrt{5(x-1)^{2} } }$

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

$\sqrt{\frac{30(x-1)}{5(x-1)^{2} } }$

We simplify the terms under the radical sign to obtain;

$\sqrt{\frac{6}{x-1} }$

Choice D is thus the correct solution

Answer 2

Answer: OPTION D

Step-by-step explanation:

You need to remember this property:

$\frac{\sqrt{x} }{\sqrt{y} }=\sqrt{\frac{x}{y} }$

And remember that:

$\frac{a}{a}=1$

Then, the first step is rewrite the expression:

$\frac{\sqrt{30(x-1)} }{\sqrt{5(x-1)^2}}$ $=\sqrt{\frac{30(x-1)}{5(x-1)^2}} }$

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

Therefore, the equivalent expression is the following:

$\sqrt{\frac{6}{(x-1)}} }$

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