(7x-9)/(x^2-25)-(3)/(x-5)=(2)/(x-5)

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Solution for (7x-9)/(x^2-25)-(3)/(x-5)=(2)/(x-5) equation: 


D( x )

x-5 = 0

x^2-25 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x^2-25 = 0

x^2-25 = 0

1*x^2 = 25 // : 1

x^2 = 25

x^2 = 25 // ^ 1/2

abs(x) = 5

x = 5 or x = -5

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

(7*x-9)/(x^2-25)-(3/(x-5)) = 2/(x-5) // - 2/(x-5)

(7*x-9)/(x^2-25)-(3/(x-5))-(2/(x-5)) = 0

(7*x-9)/(x^2-25)-3*(x-5)^-1-2*(x-5)^-1 = 0

(7*x-9)/(x^2-25)-3/(x-5)-2/(x-5) = 0

((7*x-9)*(x-5))/((x^2-25)*(x-5))+(-3*(x^2-25))/((x^2-25)*(x-5))+(-2*(x^2-25))/((x^2-25)*(x-5)) = 0

(7*x-9)*(x-5)-3*(x^2-25)-2*(x^2-25) = 0

4*x^2-2*x^2-44*x+50+120 = 0

2*x^2-44*x+170 = 0

2*x^2-44*x+170 = 0

2*(x^2-22*x+85) = 0

x^2-22*x+85 = 0

DELTA = (-22)^2-(1*4*85)

DELTA = 144

DELTA > 0

x = (144^(1/2)+22)/(1*2) or x = (22-144^(1/2))/(1*2)

x = 17 or x = 5

2*(x-5)*(x-17) = 0

(2*(x-5)*(x-17))/((x^2-25)*(x-5)) = 0

(2*(x-5)*(x-17))/((x^2-25)*(x-5)) = 0 // * (x^2-25)*(x-5)

2*(x-5)*(x-17) = 0

( x-17 )

x-17 = 0 // + 17

x = 17

( x-5 )

x-5 = 0 // + 5

x = 5

x in { 5} 

x = 17

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