Question

1. Subtract and simplify
18/y-8 - 18/8-y
2. subtract simplify if possible
v-5/v - 7v-31/11v

3. Simplify by removing factors of 1
r^2-81/(r+9)^2

4. Divide and simplify
v^2-16/25v+100 divided by v-4/20

5. find all rational numbers for which the rational expression is undefined:
-18/7w

6. solve:
2/Z+4= 1/z-6

Answer 1

1. 18 / (y - 8) - 18 / (8 - y),
Multiply numerator and denominator of
2nd fraction by -1 and get:

18 / (y - 8) + 18 / (y - 8) =
36 / (y - 8).

2. (v - 5) / v - (7v - 31) / 11v,
Common denominator = 11v:
(11v - 55 -7v + 31) / 11v,
Combine like-terms:
(4v - 24) / 11v = 4(v - 6) / 11v.

3. (r^2 - 81) / (r + 9)^2,
Factor the numerator:
(r + 9) (r - 9) / (r + 9)^2,
Multiply numerator and denomjnator by
(r + 9)^2 and get:

(r + 9)^-1 (r - 9) / 1,
Multiply numerator and denominator by
(r + 9)^1:

(r - 9) / (r + 9).

4. (v^2 - (16/25)v + 100) / (v - 4)/20
Multiply numerator and denominator by 25 and get:
(V^2 - 16V + 100) / 5(V - 4) / 4,

Multiply numerator and denominqator by
4/5 and get:
4/5(v^2 - 16v + 100) / (v - 4).

6. 2 / (z + 4) = 1 / (z - 6),
Cross multiply:
2z - 12 = z + 4,
2z - z = 4 + 12,
z = 16.

Answer 2

_4y_____ _ ___3y________
y^2+6y+5 y^2+5y+4