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