4/(x^2-1)+6/(5x^2+5x)

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Solution for 4/(x^2-1)+6/(5x^2+5x) equation: 


D( x )

5*x^2+5*x = 0

x^2-1 = 0

5*x^2+5*x = 0

5*x^2+5*x = 0

5*x^2+5*x = 0

DELTA = 5^2-(0*4*5)

DELTA = 25

DELTA > 0

x = (25^(1/2)-5)/(2*5) or x = (-25^(1/2)-5)/(2*5)

x = 0 or x = -1

x^2-1 = 0

x^2-1 = 0

1*x^2 = 1 // : 1

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

x in (-oo:-1) U (-1:0) U (0:1) U (1:+oo)

4/(x^2-1)+6/(5*x^2+5*x) = 0

5*x^2+5*x = 0

5*x^2+5*x = 0

5*x*(x+1) = 0

x+1 = 0 // - 1

x = -1

5*x*(x+1) = 0

4/(x^2-1)+6/(5*x*(x+1)) = 0

(4*5*x*(x+1))/(5*x*(x^2-1)*(x+1))+(6*(x^2-1))/(5*x*(x^2-1)*(x+1)) = 0

4*5*x*(x+1)+6*(x^2-1) = 0

26*x^2+20*x-6 = 0

26*x^2+20*x-6 = 0

2*(13*x^2+10*x-3) = 0

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

DELTA = 10^2-(-3*4*13)

DELTA = 256

DELTA > 0

x = (256^(1/2)-10)/(2*13) or x = (-256^(1/2)-10)/(2*13)

x = 3/13 or x = -1

2*(x+1)*(x-3/13) = 0

(2*(x+1)*(x-3/13))/(5*x*(x^2-1)*(x+1)) = 0

(2*(x+1)*(x-3/13))/(5*x*(x^2-1)*(x+1)) = 0 // * 5*x*(x^2-1)*(x+1)

2*(x+1)*(x-3/13) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-3/13 )

x-3/13 = 0 // + 3/13

x = 3/13

x in { -1} 

x = 3/13

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