(1/(5x+5))=(9/(x+1))-(4/5)

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Solution for (1/(5x+5))=(9/(x+1))-(4/5) equation: 


D( x )

x+1 = 0

5*x+5 = 0

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

5*x+5 = 0

5*x+5 = 0

5*x+5 = 0 // - 5

5*x = -5 // : 5

x = -5/5

x = -1

x in (-oo:-1) U (-1:+oo)

1/(5*x+5) = 9/(x+1)-(4/5) // - 9/(x+1)-(4/5)

1/(5*x+5)-(9/(x+1))+4/5 = 0

1/(5*x+5)-9*(x+1)^-1+4/5 = 0

1/(5*x+5)-9/(x+1)+4/5 = 0

(1*5*(x+1))/(5*(5*x+5)*(x+1))+(-9*5*(5*x+5))/(5*(5*x+5)*(x+1))+(4*(5*x+5)*(x+1))/(5*(5*x+5)*(x+1)) = 0

1*5*(x+1)-9*5*(5*x+5)+4*(5*x+5)*(x+1) = 0

20*x^2-220*x+40*x-220+20 = 0

20*x^2-180*x-200 = 0

20*x^2-180*x-200 = 0

20*(x^2-9*x-10) = 0

x^2-9*x-10 = 0

DELTA = (-9)^2-(-10*1*4)

DELTA = 121

DELTA > 0

x = (121^(1/2)+9)/(1*2) or x = (9-121^(1/2))/(1*2)

x = 10 or x = -1

20*(x+1)*(x-10) = 0

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

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

20*(x+1)*(x-10) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-10 )

x-10 = 0 // + 10

x = 10

x in { -1} 

x = 10

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