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Method and examples
Roots For Non-Zero Denominator
(each denominator is a non-zero polynomial)

1. Method
 = (5x-18)/(x+2)=(2x-6)/(x-1)(3x-5)/(4x-7)=(5x-9)/(6x-11)(2x-3)/(x+1)=(x)/(x+4)

2. Method
 + = (x)/(x+1)+(x+1)/(x)=(5)/(2)(x+2)/(x)+(x)/(x+2)=(10)/(3)(x+1)/(x-3)+(x-3)/(x+1)=(5)/(2)(x+3)/(x+1)+(x-1)/(x+2)=(23)/(12)(2x+3)/(x)+(4x)/(2x+3)=(13)/(3)(x+4)/(x-4)+(x-4)/(x+4)=(10)/(3)(4)/(x+2)+(-1)/(x+3)=(4)/(2x+1)(3)/(x-2)+(2)/(x-3)=(2)/(x-4)(1)/(x-2)+(2)/(x-1)=(6)/(x)(1)/(x-2)+(1)/(x+3)=(7)/(2x)(4)/(x+1)+(3)/(x-2)=(4)/(1)(2(x-2))/(x+2)+(3x+2)/(x-1)=(16)/(3)

3. Method
 2 2X+1 + + =  0 X-1 12((2x+1)/(x-1))^2-5((2x+1)/(x-1))-2=02((4x+1)/(4x-1))^2+5((4x+1)/(4x-1))-3=01((x+8)/(x))^2-6((x+8)/(x))-7=04((x-1)/(x-2))^2-20((x-1)/(x-2))+25=04((4x+1)/(4x-1))^2+1((4x+1)/(4x-1))-3=012((2x+1)/(x-1))^2-5((2x+1)/(x-1))-2=0

4. Method
 X-1 + = X 12((x)/(x-1))+12((x-1)/(x))+25=01((2x-3)/(x-1))-4((x-1)/(2x-3))-3=01((2x-1)/(x+1))-15((x+1)/(2x-1))+2=015((x+1)/(x-1))-4((x-1)/(x+1))-4=03((3x-1)/(3x+1))-2((3x+1)/(3x-1))-5=0

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