Question

((3)/(9-х²)+(1)/(х-3)):(х)/(х²-6х+9)=

Answer 1

(3)/(9-х²)+(1)/(х-3)):(х)/(х²-6х+9)
1.(3/(9-х²)+1)/(х-3)=3/(3+х)(3-х)+1/(х-3)=
 3/(3+х)(3-х)-1/(3-х)=(3-3-х)/ (3+х)(3-х) =
-х/ (3+х)(3-х)=х/(3+х)(х-3) 
2. (х/(3+х)(х-3)): (х)/(х²-6х+9)= (х/(3+х)(х-3))
(х-3)²/х=(х-3)/(х+3) 

Answer 2

To simplify the given expression:

((3)/(9-x^2) + (1)/(x-3)) / (x)/(x^2-6x+9)

First, factor the denominators to simplify:

9 - x^2 = (3 + x)(3 - x) x^2 - 6x + 9 = (x - 3)^2

Now, rewrite the expression:

((3)/(3 + x) + (1)/(x - 3)) / (x)/((x - 3)^2)

Now, you'll need to find a common denominator for the fractions in the numerator:

Common denominator for (3 + x) and (x - 3) is (3 + x)(x - 3).

Now, rewrite the expression with a common denominator:

(3(x - 3) + (1)(3 + x)) / ((x)(x - 3)^2)

Now, distribute and simplify:

(3x - 9 + 3 + x) / (x(x - 3)^2)

Combine like terms:

(4x - 6) / (x(x - 3)^2)

So, the simplified expression is:

(4x - 6) / (x(x - 3)^2)