1. solve 3-w/6-w = 3/w-6

Question

2. Find the LCM of (8+9z), (64-81z^2), and (8-9z)

3. Multiply and simplify:
7z^8/10r^2 * 100r^4/49z

4. Add and simplify

2/v + 3/v^2

5. t/5-5t=0

Answer 1

1. (3 - w) / (6 - w) = 3 / (w - 6).

Cross multiply:
3(6 - w) = (3 - w) (w - 6),
18 - 3w = 3w - 18 - w^2 + 6w,
18 - 3w = 9w - 18 - w^2,
w^2 - 3w - 9w = - 18 - 18,
w^2 - 12w = - 36,
w^2 - 12 + 36 = 0,
(w - 6)^2 = 0,
(w - 6) (w - 6) = 0,
Double root:
w - 6 = 0,
w = 6.

w - 6 = 0,
w = 6.

Solution: w = 6.

2. (8 + 9z), (64 - 81z^2), (8 - 9z),

LCM = (64 - 81z^2) = (8 + 9z) (8 - 9z).
This factor was selected because it is
divisible by each of the other 2 factors.

3. 7z^8 / 10r^2 * 100r^4 / 49z,
Rearrange the factors and get:
7z^8 / 49z * 100r^4 / 10r^2,
Reduce each fraction:
z^7 / 7 * 10r^2=
10r^2z^7 / 7.

4. 2/v + 3/v^2,
Common denominator = v^2:
(2v + 3) / v^2.

5. t/5 - 5t = 0.
Multiply both sides by 5 and get:
t - 25t = 0,
-24t = 0,
Divide both sides by -24:
t = 0.