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1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)=1/6
We move all terms to the left:
1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)-(1/6)=0
Domain of the equation: (x-1)(x-2)!=0
We move all terms containing x to the left, all other terms to the right
x-1)(x!=2
x∈R
Domain of the equation: (x-2)(x-3)!=0
We move all terms containing x to the left, all other terms to the right
x-2)(x!=3
x∈R
Domain of the equation: (x-3)(x-4)!=0We add all the numbers together, and all the variables
We move all terms containing x to the left, all other terms to the right
x-3)(x!=4
x∈R
1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)-(+1/6)=0
We get rid of parentheses
1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)-1/6=0
We multiply parentheses ..
1/(+x^2-2x-1x+2)+1/(x-2)(x-3)+1/(x-3)(x-4)-1/6=0
We calculate fractions
(1*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6)/((+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6)+(1*(+x^2-2x-1x+2)*(+x^2-4x-3x+12)*6)/((+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6)+(1*(+x^2-2x-1x+2)*(+x^2-3x-2x+6)*6)/((+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6)+(-1*(+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12))/((+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6)=0
We calculate terms in parentheses: +(1*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6)/((+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6), so:
1*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6)/((+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6
We multiply all the terms by the denominator
1*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6)
Back to the equation:
+(1*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6))
We calculate terms in parentheses: +(1*(+x^2-2x-1x+2)*(+x^2-4x-3x+12)*6)/((+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6), so:
1*(+x^2-2x-1x+2)*(+x^2-4x-3x+12)*6)/((+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6
We multiply all the terms by the denominator
1*(+x^2-2x-1x+2)*(+x^2-4x-3x+12)*6)
Back to the equation:
+(1*(+x^2-2x-1x+2)*(+x^2-4x-3x+12)*6))
We calculate terms in parentheses: +(1*(+x^2-2x-1x+2)*(+x^2-3x-2x+6)*6)/((+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6), so:
1*(+x^2-2x-1x+2)*(+x^2-3x-2x+6)*6)/((+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6
We multiply all the terms by the denominator
1*(+x^2-2x-1x+2)*(+x^2-3x-2x+6)*6)
Back to the equation:
+(1*(+x^2-2x-1x+2)*(+x^2-3x-2x+6)*6))
We calculate terms in parentheses: +(-1*(+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12))/((+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6), so:We add all the numbers together, and all the variables
-1*(+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12))/((+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6
We multiply all the terms by the denominator
-1*(+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12))
Back to the equation:
+(-1*(+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)))
2x^2+(1*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6))+(1*(+x^2-2x-1x+2)*(+x^2-4x-3x+12)*6))+(1*(+6)*6))+(-1*(+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)))-2x-1x-3x-2x+2)*(=0
We add all the numbers together, and all the variables
2x^2+(1*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6))+(1*(+x^2-2x-1x+2)*(+x^2-4x-3x+12)*6))+(1*6*6))+(-1*(+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)))-2x-1x-3x-2x+2)*(=0
We add all the numbers together, and all the variables
2x^2+(1*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)*6))+(1*(+x^2-2x-1x+2)*(+x^2-4x-3x+12)*6))+36)+(-1*(+x^2-2x-1x+2)*(+x^2-3x-2x+6)*(+x^2-4x-3x+12)))-2x-1x-3x-2x+2)*(=0
| 6(5-k)=-3(-k+8) | | P2-2p-15=0 | | 13=0.75(36+a) | | 3z+9=22 | | 3.95+0.08m=0+0.10 | | 16d=11+14d | | N2-3n=0 | | 2x-7+5x=35 | | 23+x-23=9 | | 3x^2-x=150 | | 7k-14k-17=4 | | 2/3m=28 | | 1/3+5=4/3w | | (3x+12)6=12x-5 | | 4(x-1.5)=14.2 | | 1/9p=0 | | 5*x-2.6=7.4 | | 14+13y=20y-2+ | | -2(4a+3)=-5(2-a)=3(2a+3)-7 | | X2-2x-54=9 | | 3/7j=63 | | 0.3x-0.7=0.1x-0.17 | | -4=-0.5x | | 1.50*10+4y=67 | | 1.50*15+4y=67 | | 47+4x+3=7 | | 20(x-4)=38 | | X2+4x-16=-10 | | 3.95+0.8m=8.95+.06m | | 2x=64, | | 250=5(c+20) | | 47=4+3x7 |