3/(x^2-7x+10)+2=(x-4)/(x-5)

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Solution for 3/(x^2-7x+10)+2=(x-4)/(x-5) 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)

3/(x^2-(7*x)+10)+2 = (x-4)/(x-5) // - (x-4)/(x-5)

3/(x^2-(7*x)+10)-((x-4)/(x-5))+2 = 0

3/(x^2-7*x+10)-((x-4)/(x-5))+2 = 0

3/(x^2-7*x+10)+(-1*(x-4))/(x-5)+2 = 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

3/((x-2)*(x-5))+(-1*(x-4))/(x-5)+2 = 0

3/((x-2)*(x-5))+(-1*(x-4)*(x-2))/((x-2)*(x-5))+(2*(x-2)*(x-5))/((x-2)*(x-5)) = 0

2*(x-2)*(x-5)-1*(x-4)*(x-2)+3 = 0

2*x^2-x^2+6*x-14*x-5+20 = 0

x^2-8*x+15 = 0

x^2-8*x+15 = 0

x^2-8*x+15 = 0

DELTA = (-8)^2-(1*4*15)

DELTA = 4

DELTA > 0

x = (4^(1/2)+8)/(1*2) or x = (8-4^(1/2))/(1*2)

x = 5 or x = 3

(x-3)*(x-5) = 0

((x-3)*(x-5))/((x-2)*(x-5)) = 0

((x-3)*(x-5))/((x-2)*(x-5)) = 0 // * (x-2)*(x-5)

(x-3)*(x-5) = 0

( x-3 )

x-3 = 0 // + 3

x = 3

( x-5 )

x-5 = 0 // + 5

x = 5

x in { 5}

x = 3

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