(3x)/(2x+10)=1+1/(x+5)

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Solution for (3x)/(2x+10)=1+1/(x+5) 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)

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

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

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

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

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

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

3*x^2-2*x^2+13*x-20*x-50-10 = 0

x^2-7*x-60 = 0

x^2-7*x-60 = 0

x^2-7*x-60 = 0

DELTA = (-7)^2-(-60*1*4)

DELTA = 289

DELTA > 0

x = (289^(1/2)+7)/(1*2) or x = (7-289^(1/2))/(1*2)

x = 12 or x = -5

(x+5)*(x-12) = 0

((x+5)*(x-12))/((2*x+10)*(x+5)) = 0

((x+5)*(x-12))/((2*x+10)*(x+5)) = 0 // * (2*x+10)*(x+5)

(x+5)*(x-12) = 0

( x+5 )

x+5 = 0 // - 5

x = -5

( x-12 )

x-12 = 0 // + 12

x = 12

x in { -5} 

x = 12

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