Question

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

Answer 1

D is the answer

Explanation:

`\begin{array} { c } { \sqrt { 9 - x ^ { 2 } } / \sqrt { x + 3 } \text { means the same as } \frac { \sqrt { 9 - x ^ { 2 } } } { \sqrt { x + 3 } } } \\ { \text { since it is a multiple choice question, plug in values until the right one works.} } \end{array}`

`\frac { \sqrt { 9 - x ^ { 2 } } } { \sqrt { x + 3 } } \text { where } - 3 < x \leq 3`

`x = - 2 :  \frac { \sqrt { 9 - ( - 2 ) ^ { 2 } } } { \sqrt { ( - 2 ) + 3 } } = \frac { \sqrt { 9 - 4 } } { \sqrt { 1 } } = \frac { \sqrt { 5 } } { 1 } = \sqrt { 5 }\\`

This does not equal a choice

`\begin{aligned} \text { Where } x = & - 1 : \frac { \sqrt { 9 - ( - 1 ) ^ { 2 } } } { \sqrt { ( - 1 ) + 3 } } = \frac { \sqrt { 9 - 1 } } { \sqrt { 2 } } = \frac { \sqrt { 8 } } { \sqrt { 2 } } = 2 \\ & \text { This does not equal a choice } \end{aligned}`

`\begin{aligned} \text { Where } x = & 0 : \frac { \sqrt { 9 - ( 0 ) ^ { 2 } } } { \sqrt { 9 - ( 0 ) + 3 } } = \frac { \sqrt { 9 - 0 } } { \sqrt { 3 } } = \frac { \sqrt { 9 } } { \sqrt { 3 } } = \sqrt { 3 } \\ & \text { This does not equal a choice } \end{aligned}`

`\begin{aligned} \text { Where } x = & 1 : \frac { \sqrt { 9 - ( 1 ) ^ { 2 } } } { \sqrt { ( 1 ) + 3 } } = \frac { \sqrt { 9 - 1 } } { \sqrt { 4 } } = \frac { \sqrt { 8 } } { 2 } = \sqrt { 2 } \\ & \text { This does not equal a choice } \end{aligned}`

`\begin{array} { c } { \text { Where } x = 2 : \frac { \sqrt { 9 - ( 2 ) ^ { 2 } } } { \sqrt { ( 2 ) + 3 } } = \frac { \sqrt { 9 - 4 } } { \sqrt { 5 } } = \frac { \sqrt { 5 } } { \sqrt { 5 } } = 1 } \\ { \text { Therefor, option } \mathrm { D } \text { is the answer } } \end{array}`

Answer 2

The answer is C √3 - x