Question

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

Answer 1

C.
`√(3-x)`

Explanation:

The given quotient is

`√(9-x^2)/ √(3+x)`, when
`-3<\:x\le3`

We can rewrite this as

`(√(9-x^2) )/(√(3+x) )`

We factor the numerator using difference of two squares

`\Rightarrow (√(3^2-x^2))/(√(3+x))`

`\Rightarrow (√((3-x)(3+x)))/(√((3+x)))`

`\Rightarrow (√((3-x)) √((3+x)))/(√((3+x)))`

We cancel the common factors to get;

`√(3-x)`