Divide. Start Fraction left-parenthesis Start Fraction x squared plus 6 x plus 9 over x minus 1 End Fraction right-parenthesis over left-parenthesis Start Fraction x squared minus 9 over x squared minus 2 x plus 1 End Fraction right-parenthesis End Fraction

Answer 1

To divide the given expression, we first need to simplify each fraction separately.

First, simplify the numerator of the first fraction:
x^2 + 6x + 9 factors to (x + 3)(x + 3) which simplifies to (x + 3)^2

Now, simplify the second fraction:
x^2 - 9 factors to (x + 3)(x - 3)
x^2 - 2x + 1 factors to (x - 1)^2

So the expression becomes:
(x + 3)^2 / (x - 1) / [(x + 3)(x - 3) / (x - 1)^2]

Now, divide the fractions by multiplying by the reciprocal of the second fraction:
= (x + 3)^2 / (x - 1) * (x - 1)^2 / (x + 3)(x - 3)
= (x + 3)(x + 3)(x - 1)^2 / (x + 3)(x - 3)(x - 1)
= (x + 3)(x - 1) / (x - 3)