Simplify the Complex Fractions

Question

1. 8a / 3b^2 / 6ab /5
2. 42x^2 + 14x / x - 7 / 2 + 6x / 21 - 3x
3. 9 + 3 / x / x / 4 + 1 /12
4. (x^-1 + x^-2)divided by (9x^-2)

Ans. #1: 20 / 9
Ans. #2: 42x^2 + 6x + 4 / -2x + 14
Ans. #3: 144 / x / 3x + 1

I don't know how to do #4

Answer 1

I have trouble interpreting you run-on compound fractions. How about some parentheses so we know what's what?

(x^-1 + x^-2)/(9-x^2)
(1/x + 1/x^2)/(9-x^2)
(x+1)/(x^2 (9-x^2))
This doesn't simplify much.

Answer 2

1. (8a / 3b^2) / (6ab / 5)
2. (42x^2 + 14x) / (x - 7) / (2 + 6x / 21 - 3x)
3. (9 + 3 / x) / (x / 4 + 1 /12)

Answer 3

1. (8a)/(3b^2) * (5)/(6ab) = (40a)/(18ab^3) = 20/(9b^3)

2. (14x)(3x+1)/(x-7) * 3(7-x) / (2(3x+1))
= 42x(3x+1)(7-x) / 2(x-7)(3x+1)
= -21x

3. (9x+3)/x / (3x+1)/12
= 3(3x+1)/x * 12/(3x+1)
= 36/x

Answer 4

Thank you very much, Steve :)