Question

Which choice is equivalent to the quotient below when. The problem is in the photo below.i am scared please

Answer 1

Hello from MrBillDoesMath!

Answer:

Choice C, sqrt(3-x)

Discussion:

Have no fear, MBill is here!

The quotient is

sqrt (9-x^2)  / sqrt( 3+x)  =         => as sqrt(a)/sqrt(b) = sqrt(a/b), b <> 0

sqrt (   (9-x^2)/( 3+x) )  =             => as 9 - x^2 = (3-x) * (3+x)

sqrt (  (3-x)(3+x) /(3+x) ) =           => cancel (3+x) from num. and denom.

sqrt( 3-x)

This is Choice C

Note the domain restriction -3 < x < = 3 guarantees that division by zero can't happen.

Thank you,

MrB

Answer 2

We will see that the equivalent expression is the one in C.

$\sqrt{3 - x}$

Which expression is equivalent to the quotient?

Here we start with the quotient:

$\frac{\sqrt{9 - x^2} }{\sqrt{3 + x} }$

First, we can rewrite the quotient as:

$\frac{\sqrt{9 - x^2} }{\sqrt{3 + x} } = \sqrt{\frac{9 - x^2}{3 + x}}$

Now, we can rewrite the numerator as:

9 - x^2 = 3^2 - x^2 = (3 - x)*(3 + x)

Replacing that we get:

$\frac{\sqrt{9 - x^2} }{\sqrt{3 + x} } = \sqrt{\frac{9 - x^2}{3 + x}} = \sqrt{\frac{(3 - x)*(x + 3)}{3 + x}} = \sqrt{3 - x}$

Where we can only do this in the given range because the denominator is never equal to zero.

Concluding, the correct option is C.

If you want to learn more about equivalent expressions, you can read:

https://brainly.com/question/2972832