Answer:
First, we need to factor our denominators:
x^2 - 14x + 49 = (x-7)^2
x^2 - 49 = (x+7)(x-7)
x^2 + 7x = x(x+7)
Now, we can rewrite our original expression as:
[(x+7)(x-7)] / [(x-7)^2]
and
[5(x+7)] / [x(x+7)]
Next, we can simplify by canceling out common factors, such as (x+7) in both the numerator and denominator of the second fraction:
[(x+7)(x-7)] / [(x-7)^2] * 5 / x
Simplifying further, we get:
5(x+7) / (x-7)^2
This is our final answer.
Explanation: