Question

Simplify. 9-x2/9x+27

Answer 1

ANSWER


`(3 - x)/(9)`

EXPLANATION

The given expression is


`\frac{9 - {x}^(2) }{9x + 27}`

We rewrite as a difference of two squares to get,


`= \frac{ {3}^(2) - {x}^(2) }{9x + 27}`

Recall that,


`a^2-b^2=(a - b)(a+ b)`

We factor to obtain,


`= ((3 - x)(3 + x))/(9(x + 3))`

We now cancel out the common factors to get,


`= (3 - x)/(9)`

Answer 2

(3-x)/9

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