I need some help with algebra please

I'm horrible with algebra..so please help me with these! Thanks

1. Write an equation for the translation of y = 4/x that has the asymptotes x = 7 and y = 6.

a. y = 4/x-6 + 7
b. y = 4/x+7 + 6
c. y = 4/x-7 + 6
d. y = 4/x+6 + 7

2. y = (x + 6)(x + 2)(x + 8)/(x + 9)(x + 7)

a. x = 6, x = 2, x = 8
b. x = 9, x = 7
c. x = -9, x = -7
d. x = -6, x = -2, x = -8

3. y = x - 8/x^2 + 6x - 7

a. x = 1, x = 7
b. x = 8
c. x = 1, x = -7
d. x = -1, x = 7

1) C

2) if you want roots then the answer is D

3) again, if you want roots, B

1. The purpose of an asymptote is to know that what values can x take. Having an asymptote x = 7 means that x should not equal to 7 or x - 7 should not equal to 0. The y asymptote works as a limit for the equation. As x goes to infinity 4 / (x-7) will go to 0. However you asymptote is y = 6 so the final equation will be: y = 4/x-7 + 6 which is c

2. By looking at the numerator you can see which numbers make the value of the fraction 0.
Either x + 6 = 0 or x + 2 = 0 or x + 8 = 0. Thus the solutions are x = -6, x = -2, x = -8 which is d

3. This example tries to confuse. No matter what the denominator is the solutions have always to do with the numerator. Thus the correct answer is b) x = 8. You should check however the denominator for this value of x because if it is 0 it would have no solution