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

Question

asked May 21, 2020 27.4k views

2 Answers

Ademola · Answer 1 · 2020-05-21T11:05:53+0000

Answer:

Choice D

Explanation:

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

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

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

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

We simplify the terms under the radical sign to obtain;

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

Choice D is thus the correct solution

Anastazia · Answer 2 · 2020-05-25T18:07:02+0000

Answer: OPTION D

Explanation:

You need to remember this property:

$(√(x) )/(√(y) )=\sqrt{(x)/(y) }$

And remember that:

(a)/(a)=1

Then, the first step is rewrite the expression:

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

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

Therefore, the equivalent expression is the following:

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

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