Please help! I can't seem to understand these math questions.?

Question

1.

These first ones won't seem to space right. I will put a / in the middle of where they're suppossed to be.

2z-1 / 3z-5 / 2z-3

________ - _________ + ________

z^2+z-6 / z^2-2z-15 / z^2-7z+10

2.

12a^2+26a+12

________________

6-5a-6a^2

3.

1 1

_ + _

c d

________

c d

_ - _

d c

4.

Solve proportion

X+2 / x-4

____ = ____

x+6 / x-2

5.

1 / 7 / 1

_ + _ = + _

2 / y / y

Answer 1

4.  Cross multiply the proportion

(x+2)(x-2) = (x+6)(x-4)

Distribute  

x^2 + 2x - 2x - 4 = x^2 + 6x - 4x - 24

Subtract the x^2 from both sides to cancel and then Combine like terms for the rest:  

- 4 = 2x - 24

Add 24 to both sides:

  - 4 + 24 = 2x - 24 + 24

simplify:

  20 = 2x

divide by 2:  

x = 10

#3 (if I am reading your problem right)

1/c + 1/d

-------------

c/d - d/c

Multiply everything on the top and bottom by the common denominator (cd) or (cd/1)

(cd/1)(1/c) + (cd/1)(1/d)

---------------------------------

(cd/1)(c/d) - (cd/1)(d/c)

When written correctly as real fractions, you can see to cancel the like letters on top and bottom, so you get

d + c

--------------

c^2 - d^2

Factor the denominator as the difference of squares

d + c

-------------------

(c - d) (c + d)

Since d + c on the top is the same factor as c + d on the bottom, they can cancel, leaving the answer

1

------

c - d

for #5, do you have an extra plus sign?

if the problem is 1/2 + 7/y = 1/y

you can also multiply every term by the common denominator (2y) or (2y/1)  to cancel the fractions

(2y/1)(1/2) + (2y/1)(7/y) = (2y/1)(1/y)

when written as real fractions, you can see to cancel and get

y + 14 = 2

subtract 14 from each side

y + 14 - 14 = 2 - 14

so y = - 12

Answer 2

Here is one:

12a^2+26a+12

________________

6-5a-6a^2

factor each part:

top = 2(6a^2 + 13a + 6) = 2(3a + 2)(2a + 3)

bottom = (3 + 2a)(2 - 3a)

now since 3 + 2a = 2a + 3, cancel one from the top and bottom to get

2(3a + 2) over (2 - 3a)