Algebra 2 help...............?

Question

1. Which is equivalent to z + 1 / (z - 1) - z - 1 / (z + 2)
A. 6z / (z - 2)(z + 2)
B. 6z + 4 / (z - 2)(z + 2)
C. 2 / z
D. 2 / (z - 2)(z + 2)

2. Which is the completely factored form of 8r^3 - 125s^3?
A. (2r + 5s)(4r^2 - 10rs + 25s^2)
B. (2r + 5s)^3
C. (2r - 5s)(4r^2 + 10rs + 25s^2)
D. (2r - 5s)(4r^2 + 20rs + 25r^2)

3. Solve : 12 - √4x + 9) = 5

Answer 1

1).The expression is z + 1 / (z - 1) - z - 1 / (z + 2)

Combine like terms

= (z - z) + {1 / (z - 1) - 1 / (z + 2)}

= 1 / (z - 1) - 1 / (z + 2)                          (Simplify)

L.C.M of  (z - 1) and (z + 2) = (z - 1)(z + 2)

= 1(z + 2)-1(z - 1) / (z - 1)(z + 2)

= (z + 2 - z + 1) / (z - 1)(z + 2)               (Multiply)

= (2 + 1) / (z - 1)(z + 2)                          (Simplify)

= 3 / (z - 1)(z + 2)

The given options are no match the above solution.

Answer 2

2). The expression is 8r^3 - 125s^3

Rewrite the expression (2r)^3 - (5s)^3

The above expression compare with a^3 - b^3 = (a - b)(a^2 +ab +b^2)

Substitute a  = 2r and b = 5s

(2r)^3 - (5s)^3 = (2r - 5s)((2r)^2 +2r(5s) +(5s)^2)

                       = (2r - 5s)((2r)^2 +10rs +(5s)^2)               (Multiply)

                       = (2r - 5s)(4r^2 +10rs +25s^2)                   (Simplify)

Option "C" is the right answer.