3 problems.... Please help me understand...?

Question

1. Factor completely:
x^2 + 12x + 36

2. Subtract: Express your answer in simplest form:
(2x) over (x - 5) - (10) over (x - 5)

3. Divide:
(x^2 - 25y^2) over (5x^2 + 25y) divided by (x^2 - 5xy)

Answer 1

1)(x+6)²

2)2x/(x-5) - 10/(x-5) = 2(x-5)/(x-5) = 2

3 (x²-25y²)/(5x²+25y) /(x²-5xy)
(x-5y)(x+5y)/5x(x²+5y)(x-5y)
(x+5y)/5x(x²+5y)

Answer 2

x^2 + 12 x + 36 factor into this format
(x )(x )
now ask yourself what numbers multiplied together = 36, lets start with positive ones; they are
36 & 1
18 & 2
12 & 3
9 & 4
6 & 6
note how these are listed and understand how I got these pairs.
now of the above pairs, which pairs when added together = 12? - clearly 6 & 6. The factor then is
(x + 6)(x+6)
work this over and over until you understand factoring as you will need it again and again

2. This is simple fractions of the format a/b - c / b where b=(x-5); the answer is (a-c)/b Understand this and you will conclude that the answer is (2x-10)/(x-5) and then you see from factoring it also is 2(x-5)/(x-5) and this simplifies to 2

Answer 3

1. (x+6)(x+6)
2. 2x-10/(x - 5)
3. 1/x^2-5x