Using complete sentences, explain each step in simplifying the ratio of [(x2)+ 8x]/[x2 + (10x) + 16]?i cant seem to get this!

To simplify the ratio, we'll focus on the numerator and
denominator,  separately.

We notice that the denominator is
a quadratic and we'll apply the quadratic formula to calculate it's
roots.

The quadratic formula
is:

x1 = [-b+sqrt(b^2 -
4ac)]/2a

x2 = [-b-sqrt(b^2 -
4ac)]/2a

a,b,c, are the coefficients of the quadratic: ax^2
+ bx + c.

We'll identify
a,b,c:

a = 1

b =
10

c = 16

We'll substitute
them into the formula:

x1 = [-b+sqrt(b^2 -
4ac)]/2a

x1 = [-10+sqrt(100 -
64)]/2

x1 = (-10+sqrt36)/2

x1
= (-10+6)/2

x1 = -2

x2 =
(-10-6)/2

x2 = -8

Now, we'll
write the quadratic:

a(x - x1)(x - x2) =
1*(x+2)(x+8)

The denominator will
become:

x^2 + 10x + 16 =
(x+2)(x+8)

We notice that we can factorize the numerator,
by x:

x^2 + 8x = x(x+8)

We'll
re-write the ratio:

(x^2 + 8x)/(x^2 + 10x + 16) =
x(x+8)/(x+2)(x+8)

We'll reduce like terms, namely
(x+8):

(x^2 + 8x)/(x^2 + 10x + 16) =
x/(x+2)