Help!

I'm interpreting this very liberally, but we can write this as :

[(3x^2 - 21x) (15x + 20)] / [ (6x + 8) (x^3 - 14x^2 + 49x) ]       factor, where possible

[ 3x ( x - 7) * 5 (3x + 4)] / [ 2 (3x + 4) * x ( x^2 - 14x + 49)] 

[ 3x ( x - 7) * 5 (3x + 4)] / [ 2 (3x + 4) * x ( x - 7)^2 ] 

[15x (x - 7) (3x + 4)] / [ 2x (3x + 4) (x - 7)^2 ]

[15/2]  / (x - 7)

15 / ( 2x - 14)      x cannot be equal  to -4/3 , 0   or  7   because any of these values makes the original expression 0 in the denominator

http://www.wolframalpha.com/input/?i=%283x%5E2-21x%2F6x%2B8%29%2F%28x%5E3-14x%5E2%2B49x%2F15x%2B20%29

Simplify the following:
(3 x^2-21 1/6 x x+8)/(x^3+49 1/15 x x-14 x^2+20)

Combine powers. (49 x x)/15 = (49 x^(1+1))/15:
(3 x^2-21 1/6 x x+8)/(x^3+(49 x^1+1)/15-14 x^2+20)

1+1 = 2:
(3 x^2-21 1/6 x x+8)/(x^3+(49 x^2)/15-14 x^2+20)

Put each term in x^3+(49 x^2)/15-14 x^2+20 over the common denominator 15: x^3+(49 x^2)/15-14 x^2+20  =  (15 x^3)/15+(49 x^2)/15-(210 x^2)/15+300/15:
(3 x^2-21 1/6 x x+8)/((15 x^3)/15+(49 x^2)/15-(210 x^2)/15+300/15)

(15 x^3)/15+(49 x^2)/15-(210 x^2)/15+300/15 = (15 x^3+49 x^2-210 x^2+300)/15:
(3 x^2-21 1/6 x x+8)/((15 x^3+49 x^2-210 x^2+300)/15)

49 x^2-210 x^2 = -161 x^2:
(3 x^2-21 1/6 x x+8)/((15 x^3+-161 x^2+300)/15)

-(21 x x)/6 = -(21 x^2)/6:
(3 x^2+-(21 x^2)/6+8)/((15 x^3-161 x^2+300)/15)

The gcd of -21 and 6 is 3, so (-21 x^2)/6 = ((3 (-7)) x^2)/(3×2) = 3/3×(-7 x^2)/2 = (-7 x^2)/2:
(3 x^2+(-7 x^2)/2+8)/((15 x^3-161 x^2+300)/15)

Put each term in 3 x^2-(7 x^2)/2+8 over the common denominator 2: 3 x^2-(7 x^2)/2+8  =  (6 x^2)/2-(7 x^2)/2+16/2:
((6 x^2)/2-(7 x^2)/2+16/2)/((15 x^3-161 x^2+300)/15)

(6 x^2)/2-(7 x^2)/2+16/2 = (6 x^2-7 x^2+16)/2:
((6 x^2-7 x^2+16)/2)/((15 x^3-161 x^2+300)/15)

6 x^2-7 x^2 = -x^2:
(-x^2+16)/(2 (15 x^3-161 x^2+300)/15)

Factor -1 out of 16-x^2:
-(x^2-16)/(2 (15 x^3-161 x^2+300)/15)

x^2-16 = x^2-4^2:
-(x^2-4^2)/(2 (15 x^3-161 x^2+300)/15)

Factor the difference of two squares. x^2-4^2 = (x-4) (x+4):
-(x-4) (x+4)/(2 (15 x^3-161 x^2+300)/15)

Multiply the numerator by the reciprocal of the denominator, -((x-4) (x+4))/(2 (15 x^3-161 x^2+300)/15) = (-(x-4) (x+4))/2×15/(15 x^3-161 x^2+300):
Answer: | -(15 (x-4) (x+4))/(2 (15 x^3-161 x^2+300))

Solve for x:
(240-15 x^2)/(30 x^3-322 x^2+600) = 0

Multiply both sides by 30 x^3-322 x^2+600:
240-15 x^2 = 0

The left hand side factors into a product with three terms:
-15 (x-4) (x+4) = 0

Divide both sides by -15:
(x-4) (x+4) = 0

Split into two equations:
x-4 = 0 or x+4 = 0

Add 4 to both sides:
x = 4 or x+4 = 0

Subtract 4 from both sides:
Answer: | x = 4 or x = -4

Hallo StingSniperscope

Omi 67 :DD

StingSniperscope: You should separate your terms by proper brackets:

Simplify the following:
(3 x^2-21 x)/(((6 x+8) (x^3-14 x^2+49 x))/(15 x+20))

Multiply the numerator of (3 x^2-21 x)/(((6 x+8) (x^3-14 x^2+49 x))/(15 x+20)) by the reciprocal of the denominator. (3 x^2-21 x)/(((6 x+8) (x^3-14 x^2+49 x))/(15 x+20)) = ((3 x^2-21 x) (15 x+20))/((6 x+8) (x^3-14 x^2+49 x)):
((3 x^2-21 x) (15 x+20))/((6 x+8) (x^3-14 x^2+49 x))

Factor 2 out of 6 x+8:
((3 x^2-21 x) (15 x+20))/(2 (3 x+4) (x^3-14 x^2+49 x))

Factor 5 out of 15 x+20:
(5 (3 x+4) (3 x^2-21 x))/(2 (3 x+4) (x^3-14 x^2+49 x))

Factor 3 x out of 3 x^2-21 x:
(5×3 x (x-7) (3 x+4))/(2 (3 x+4) (x^3-14 x^2+49 x))

Factor x out of x^3-14 x^2+49 x:
(3×5 x (x-7) (3 x+4))/(2 x (x^2-14 x+49) (3 x+4))

The factors of 49 that sum to -14 are -7 and -7. So, x^2-14 x+49 = (x-7) (x-7):
(3×5 x (x-7) (3 x+4))/(2 x (x-7) (x-7) (3 x+4))

(x-7) (x-7) = (x-7)^2:
(3×5 x (x-7) (3 x+4))/(2 x (x-7)^2 (3 x+4))

(3 x (x-7)×5 (3 x+4))/(2 (3 x+4) x (x-7)^2) = ((3 x+4) x)/((3 x+4) x)×(3 (x-7)×5)/(2 (x-7)^2) = (3 (x-7)×5)/(2 (x-7)^2):
(3×5 (x-7))/(2 (x-7)^2)

3×5  =  15:
(15 (x-7))/(2 (x-7)^2)

Cancel terms. (15 (x-7))/(2 (x-7)^2)  =  15/(2 (x-7)^(2-1)):
15/(2 (x-7)^2-1)

2-1 = 1:
Answer: | 15/(2 (x-7))