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Do you have to do this everyday?

IDK

P.S. Whoever gave you this problem must be nuts!!!!! Here it goes and good luck:

Simplify the following:
(2 x^7)/3-(19 x^6)/6-(509 x^5)/22-(2875 x^4)/22+(15331 x^3)/66+(19447 x^2)/33-(6618 x)/11-700/11

Put each term in (2 x^7)/3-(19 x^6)/6-(509 x^5)/22-(2875 x^4)/22+(15331 x^3)/66+(19447 x^2)/33-(6618 x)/11-700/11 over the common denominator 66: (2 x^7)/3-(19 x^6)/6-(509 x^5)/22-(2875 x^4)/22+(15331 x^3)/66+(19447 x^2)/33-(6618 x)/11-700/11  =  (44 x^7)/66-(209 x^6)/66-(1527 x^5)/66-(8625 x^4)/66+(15331 x^3)/66+(38894 x^2)/66-(39708 x)/66-4200/66:
(44 x^7)/66-(209 x^6)/66-(1527 x^5)/66-(8625 x^4)/66+(15331 x^3)/66+(38894 x^2)/66-(39708 x)/66-4200/66

(44 x^7)/66-(209 x^6)/66-(1527 x^5)/66-(8625 x^4)/66+(15331 x^3)/66+(38894 x^2)/66-(39708 x)/66-4200/66 = (44 x^7-209 x^6-1527 x^5-8625 x^4+15331 x^3+38894 x^2-39708 x-4200)/66:
(44 x^7-209 x^6-1527 x^5-8625 x^4+15331 x^3+38894 x^2-39708 x-4200)/66

The possible rational roots of 44 x^7-209 x^6-1527 x^5-8625 x^4+15331 x^3+38894 x^2-39708 x-4200 are x = ±1/44, x = ±3/44, x = ±5/44, x = ±7/44, x = ±15/44, x = ±21/44, x = ±25/44, x = ±35/44, x = ±75/44, x = ±105/44, x = ±175/44, x = ±525/44, x = ±1/22, x = ±3/22, x = ±5/22, x = ±7/22, x = ±15/22, x = ±21/22, x = ±25/22, x = ±35/22, x = ±75/22, x = ±105/22, x = ±175/22, x = ±525/22, x = ±1/11, x = ±2/11, x = ±3/11, x = ±4/11, x = ±5/11, x = ±6/11, x = ±7/11, x = ±8/11, x = ±10/11, x = ±12/11, x = ±14/11, x = ±15/11, x = ±20/11, x = ±21/11, x = ±24/11, x = ±25/11, x = ±28/11, x = ±30/11, x = ±35/11, x = ±40/11, x = ±42/11, x = ±50/11, x = ±56/11, x = ±60/11, x = ±70/11, x = ±75/11, x = ±84/11, x = ±100/11, x = ±105/11, x = ±120/11, x = ±140/11, x = ±150/11, x = ±168/11, x = ±175/11, x = ±200/11, x = ±210/11, x = ±280/11, x = ±300/11, x = ±350/11, x = ±420/11, x = ±525/11, x = ±600/11, x = ±700/11, x = ±840/11, x = ±1050/11, x = ±1400/11, x = ±2100/11, x = ±4200/11, x = ±1/4, x = ±3/4, x = ±5/4, x = ±7/4, x = ±15/4, x = ±21/4, x = ±25/4, x = ±35/4, x = ±75/4, x = ±105/4, x = ±175/4, x = ±525/4, x = ±1/2, x = ±3/2, x = ±5/2, x = ±7/2, x = ±15/2, x = ±21/2, x = ±25/2, x = ±35/2, x = ±75/2, x = ±105/2, x = ±175/2, x = ±525/2, x = ±1, x = ±2, x = ±3, x = ±4, x = ±5, x = ±6, x = ±7, x = ±8, x = ±10, x = ±12, x = ±14, x = ±15, x = ±20, x = ±21, x = ±24, x = ±25, x = ±28, x = ±30, x = ±35, x = ±40, x = ±42, x = ±50, x = ±56, x = ±60, x = ±70, x = ±75, x = ±84, x = ±100, x = ±105, x = ±120, x = ±140, x = ±150, x = ±168, x = ±175, x = ±200, x = ±210, x = ±280, x = ±300, x = ±350, x = ±420, x = ±525, x = ±600, x = ±700, x = ±840, x = ±1050, x = ±1400, x = ±2100, x = ±4200. Of these, x = 1, x = 2 and x = -2 are roots. This gives x-1, x-2 and x+2 as all linear factors:
(((x-1) (x-2) (x+2) (44 x^7-209 x^6-1527 x^5-8625 x^4+15331 x^3+38894 x^2-39708 x-4200))/((x-1) (x-2) (x+2)))/(66)

 |  |
x | - | 2 |  | 44 x^6 | - | 121 x^5 | - | 1769 x^4 | - | 12163 x^3 | - | 8995 x^2 | + | 20904 x | + | 2100
44 x^7 | - | 209 x^6 | - | 1527 x^5 | - | 8625 x^4 | + | 15331 x^3 | + | 38894 x^2 | - | 39708 x | - | 4200
44 x^7 | - | 88 x^6 |  |  |  |  |  |  |  |  |  |  |  |
 |  | -121 x^6 | - | 1527 x^5 |  |  |  |  |  |  |  |  |  |
 |  | -121 x^6 | + | 242 x^5 |  |  |  |  |  |  |  |  |  |
 |  |  |  | -1769 x^5 | - | 8625 x^4 |  |  |  |  |  |  |  |
 |  |  |  | -1769 x^5 | + | 3538 x^4 |  |  |  |  |  |  |  |
 |  |  |  |  |  | -12163 x^4 | + | 15331 x^3 |  |  |  |  |  |
 |  |  |  |  |  | -12163 x^4 | + | 24326 x^3 |  |  |  |  |  |
 |  |  |  |  |  |  |  | -8995 x^3 | + | 38894 x^2 |  |  |  |
 |  |  |  |  |  |  |  | -8995 x^3 | + | 17990 x^2 |  |  |  |
 |  |  |  |  |  |  |  |  |  | 20904 x^2 | - | 39708 x |  |
 |  |  |  |  |  |  |  |  |  | 20904 x^2 | - | 41808 x |  |
 |  |  |  |  |  |  |  |  |  |  |  | 2100 x | - | 4200
 |  |  |  |  |  |  |  |  |  |  |  | 2100 x | - | 4200
 |  |  |  |  |  |  |  |  |  |  |  |  |  | 0:
((44 x^6-121 x^5-1769 x^4-12163 x^3-8995 x^2+20904 x+2100)/((x-1) (x+2)) (x-1) (x-2) (x+2))/(66)

 |  |
x | - | 1 |  | 44 x^5 | - | 77 x^4 | - | 1846 x^3 | - | 14009 x^2 | - | 23004 x | - | 2100
44 x^6 | - | 121 x^5 | - | 1769 x^4 | - | 12163 x^3 | - | 8995 x^2 | + | 20904 x | + | 2100
44 x^6 | - | 44 x^5 |  |  |  |  |  |  |  |  |  |
 |  | -77 x^5 | - | 1769 x^4 |  |  |  |  |  |  |  |
 |  | -77 x^5 | + | 77 x^4 |  |  |  |  |  |  |  |
 |  |  |  | -1846 x^4 | - | 12163 x^3 |  |  |  |  |  |
 |  |  |  | -1846 x^4 | + | 1846 x^3 |  |  |  |  |  |
 |  |  |  |  |  | -14009 x^3 | - | 8995 x^2 |  |  |  |
 |  |  |  |  |  | -14009 x^3 | + | 14009 x^2 |  |  |  |
 |  |  |  |  |  |  |  | -23004 x^2 | + | 20904 x |  |
 |  |  |  |  |  |  |  | -23004 x^2 | + | 23004 x |  |
 |  |  |  |  |  |  |  |  |  | -2100 x | + | 2100
 |  |  |  |  |  |  |  |  |  | -2100 x | + | 2100
 |  |  |  |  |  |  |  |  |  |  |  | 0:
((44 x^5-77 x^4-1846 x^3-14009 x^2-23004 x-2100)/(x+2) (x-1) (x-2) (x+2))/(66)

 |  |
x | + | 2 |  | 44 x^4 | - | 165 x^3 | - | 1516 x^2 | - | 10977 x | - | 1050
44 x^5 | - | 77 x^4 | - | 1846 x^3 | - | 14009 x^2 | - | 23004 x | - | 2100
44 x^5 | + | 88 x^4 |  |  |  |  |  |  |  |
 |  | -165 x^4 | - | 1846 x^3 |  |  |  |  |  |
 |  | -165 x^4 | - | 330 x^3 |  |  |  |  |  |
 |  |  |  | -1516 x^3 | - | 14009 x^2 |  |  |  |
 |  |  |  | -1516 x^3 | - | 3032 x^2 |  |  |  |
 |  |  |  |  |  | -10977 x^2 | - | 23004 x |  |
 |  |  |  |  |  | -10977 x^2 | - | 21954 x |  |
 |  |  |  |  |  |  |  | -1050 x | - | 2100
 |  |  |  |  |  |  |  | -1050 x | - | 2100
 |  |  |  |  |  |  |  |  |  | 0:
Answer: |  (44 x^4-165 x^3-1516 x^2-10977 x-1050 (x-1) (x-2) (x+2))/66

\(\frac{2x^7}{3}-\frac{16x^6}{6}-\frac{509x^5}{22}-\frac{2875x^4}{22}+\frac{15331x^3}{66}+\frac{19447x^2}{33}-\frac{6618x}{11}-\frac{700}{11}\)

= \(\frac{44x^7}{66}-\frac{176x^6}{66}-\frac{1527x^5}{66}-\frac{8625x^4}{66}+\frac{15331x^3}{66}+\frac{38894x^2}{66}-\frac{39708x}{66}-\frac{4200}{66}\)

= \(\frac{44x^7-176x^6-1527x^5-8625x^4+15331x^3+38894x^2-39708x-4200}{66}\)