Respuesta :

wegnerkolmp2741o

Answer:

(3-x)/9

Step-by-step explanation:

(9-x^2)

---------------

9x+27

Factor the numerator and denominator

(3-x)  (3+x)

----------------

9(x+3)

Rewriting the denominator as 3+x

(3-x)  (3+x)

----------------

9(3+x)

Canceling 3+x from the numerator and denominator

(3-x)  

----------------

9

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ANSWER

[tex] \frac{3 - x}{9} [/tex]

EXPLANATION

The given expression is

[tex] \frac{9 - {x}^{2} }{9x + 27} [/tex]

We rewrite as a difference of two squares to get,

[tex] = \frac{ {3}^{2} - {x}^{2} }{9x + 27} [/tex]

Recall that,

[tex]a^2-b^2=(a - b)(a+ b)[/tex]

We factor to obtain,

[tex] = \frac{(3 - x)(3 + x)}{9(x + 3)} [/tex]

We now cancel out the common factors to get,

[tex] = \frac{3 - x}{9} [/tex]

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