Algebra
posted by Anonymous on .
1. solve 3w/6w = 3/w6
2. Find the LCM of (8+9z), (6481z^2), and (89z)
3. Multiply and simplify:
7z^8/10r^2 * 100r^4/49z
4. Add and simplify
2/v + 3/v^2
5. t/55t=0

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.