((x-8)/(x+5))=((x-1)/(2x+10))

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Solution for ((x-8)/(x+5))=((x-1)/(2x+10)) equation: 


D( x )

x+5 = 0

2*x+10 = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

2*x+10 = 0

2*x+10 = 0

2*x+10 = 0 // - 10

2*x = -10 // : 2

x = -10/2

x = -5

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

(x-8)/(x+5) = (x-1)/(2*x+10) // - (x-1)/(2*x+10)

(x-8)/(x+5)-((x-1)/(2*x+10)) = 0

(x-8)/(x+5)+(-1*(x-1))/(2*x+10) = 0

((x-8)*(2*x+10))/((x+5)*(2*x+10))+(-1*(x-1)*(x+5))/((x+5)*(2*x+10)) = 0

(x-8)*(2*x+10)-1*(x-1)*(x+5) = 0

x^2-10*x-75 = 0

x^2-10*x-75 = 0

x^2-10*x-75 = 0

DELTA = (-10)^2-(-75*1*4)

DELTA = 400

DELTA > 0

x = (400^(1/2)+10)/(1*2) or x = (10-400^(1/2))/(1*2)

x = 15 or x = -5

(x+5)*(x-15) = 0

((x+5)*(x-15))/((x+5)*(2*x+10)) = 0

((x+5)*(x-15))/((x+5)*(2*x+10)) = 0 // * (x+5)*(2*x+10)

(x+5)*(x-15) = 0

( x+5 )

x+5 = 0 // - 5

x = -5

( x-15 )

x-15 = 0 // + 15

x = 15

x in { -5} 

x = 15

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