7x/(x^2-36)+8/(x+6)=1/(x-6)

Solution for 7x/(x^2-36)+8/(x+6)=1/(x-6) equation:

D( x )

x-6 = 0

x^2-36 = 0

x+6 = 0

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

x^2-36 = 0

x^2-36 = 0

1*x^2 = 36 // : 1

x^2 = 36

x^2 = 36 // ^ 1/2

abs(x) = 6

x = 6 or x = -6

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

x in (-oo:-6) U (-6:6) U (6:+oo)

(7*x)/(x^2-36)+8/(x+6) = 1/(x-6) // - 1/(x-6)

(7*x)/(x^2-36)+8/(x+6)-(1/(x-6)) = 0

(7*x)/(x^2-36)+8/(x+6)-(x-6)^-1 = 0

(7*x)/(x^2-36)+8/(x+6)-1/(x-6) = 0

(7*x*(x+6)*(x-6))/((x^2-36)*(x+6)*(x-6))+(8*(x^2-36)*(x-6))/((x^2-36)*(x+6)*(x-6))+(-1*(x^2-36)*(x+6))/((x^2-36)*(x+6)*(x-6)) = 0

7*x*(x+6)*(x-6)+8*(x^2-36)*(x-6)-1*(x^2-36)*(x+6) = 0

15*x^3-x^3-48*x^2-6*x^2-540*x+36*x+216+1728 = 0

14*x^3-54*x^2-504*x+1944 = 0

14*x^3-54*x^2-504*x+1944 = 0

2*(7*x^3-27*x^2-252*x+972) = 0

7*x^3-27*x^2-252*x+972 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 9, -9, 12, -12, 18, -18, 27, -27, 36, -36, 54, -54, 81, -81, 108, -108, 162, -162, 243, -243, 324, -324, 486, -486, 972, -972 }

1

x = 1

7*x^3-27*x^2-252*x+972 = 700

1

-1

x = -1

7*x^3-27*x^2-252*x+972 = 1190

-1

2

x = 2

7*x^3-27*x^2-252*x+972 = 416

2

-2

x = -2

7*x^3-27*x^2-252*x+972 = 1312

-2

3

x = 3

7*x^3-27*x^2-252*x+972 = 162

3

-3

x = -3

7*x^3-27*x^2-252*x+972 = 1296

-3

4

x = 4

7*x^3-27*x^2-252*x+972 = -20

4

-4

x = -4

7*x^3-27*x^2-252*x+972 = 1100

-4

6

x = 6

7*x^3-27*x^2-252*x+972 = 0

6

x-6

7*x^2+15*x-162

7*x^3-27*x^2-252*x+972

x-6

42*x^2-7*x^3

15*x^2-252*x+972

90*x-15*x^2

972-162*x

162*x-972

0

7*x^2+15*x-162 = 0

DELTA = 15^2-(-162*4*7)

DELTA = 4761

DELTA > 0

x = (4761^(1/2)-15)/(2*7) or x = (-4761^(1/2)-15)/(2*7)

x = 27/7 or x = -6

x in { -6, 27/7, 6} 

2*(x+6)*(x-27/7)*(x-6) = 0

(2*(x+6)*(x-27/7)*(x-6))/((x^2-36)*(x+6)*(x-6)) = 0

(2*(x+6)*(x-27/7)*(x-6))/((x^2-36)*(x+6)*(x-6)) = 0 // * (x^2-36)*(x+6)*(x-6)

2*(x+6)*(x-27/7)*(x-6) = 0

( x+6 )

x+6 = 0 // - 6

x = -6

( x-27/7 )

x-27/7 = 0 // + 27/7

x = 27/7

( x-6 )

x-6 = 0 // + 6

x = 6

x in { -6} 

x in { 6} 

x = 27/7