x^2 + 9x + 20 over x^2 -25 divided by x +4 over x - 4

How to do this really confusing i need to simplify the rational expression

I read that as

(x2+9x+20)/(x^2-25) ÷ (x+4)/(x-4)
= (x+4)(x+5)/((x+5)(x-5)) ( x-4)/(x+4)
= (x-4)/(x-5) , x ≠ ±5,±4

To simplify the rational expression (x^2 + 9x + 20)/(x^2 - 25) ÷ (x + 4)/(x - 4), we can convert it into a multiplication problem by multiplying the numerator by the reciprocal of the denominator.

Step 1: Factoring the expressions
First, let's factor the numerator and denominator expressions to simplify them.

For the numerator, x^2 + 9x + 20, we need to find two numbers whose sum is 9 and whose product is 20. The numbers 4 and 5 satisfy these conditions, so we can factor the numerator as (x + 4)(x + 5).

For the denominator, x^2 - 25, we can use the difference of squares formula to factor it as (x - 5)(x + 5).

Step 2: Rewriting the expression
Now, we can rewrite our expression as multiplication:

[(x + 4)(x + 5)] / [(x - 5)(x + 5)] * [(x - 4)/(x + 4)]

Step 3: Simplifying the expression
Next, we can cancel out common factors between the numerator and denominator.

(x + 4) and (x - 4) cancel out, leaving us with:

(x + 5)/(x - 5)

Thus, the simplified expression is (x + 5)/(x - 5).