2/(x-5)-6/(x^2-7x+10)

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Solution for 2/(x-5)-6/(x^2-7x+10) equation: 


D( x )

x-5 = 0

x^2-(7*x)+10 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x^2-(7*x)+10 = 0

x^2-(7*x)+10 = 0

x^2-7*x+10 = 0

x^2-7*x+10 = 0

DELTA = (-7)^2-(1*4*10)

DELTA = 9

DELTA > 0

x = (9^(1/2)+7)/(1*2) or x = (7-9^(1/2))/(1*2)

x = 5 or x = 2

x in (-oo:2) U (2:5) U (5:+oo)

2/(x-5)-(6/(x^2-(7*x)+10)) = 0

2/(x-5)-6*(x^2-7*x+10)^-1 = 0

2/(x-5)-6/(x^2-7*x+10) = 0

x^2-7*x+10 = 0

x^2-7*x+10 = 0

x^2-7*x+10 = 0

DELTA = (-7)^2-(1*4*10)

DELTA = 9

DELTA > 0

x = (9^(1/2)+7)/(1*2) or x = (7-9^(1/2))/(1*2)

x = 5 or x = 2

(x-2)*(x-5) = 0

2/(x-5)-6/((x-2)*(x-5)) = 0

(2*(x-2))/((x-5)*(x-2))-6/((x-5)*(x-2)) = 0

2*(x-2)-6 = 0

2*x-10 = 0

(2*x-10)/((x-5)*(x-2)) = 0

(2*x-10)/((x-5)*(x-2)) = 0 // * (x-5)*(x-2)

2*x-10 = 0

2*x-10 = 0 // + 10

2*x = 10 // : 2

x = 10/2

x = 5

x in { 5} 

x belongs to the empty set

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