(6/(4m+5))-(6/(m-2))=(1/(4m^2-3m-10))

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Solution for (6/(4m+5))-(6/(m-2))=(1/(4m^2-3m-10)) equation: 


D( m )

m-2 = 0

4*m+5 = 0

4*m^2-(3*m)-10 = 0

m-2 = 0

m-2 = 0

m-2 = 0 // + 2

m = 2

4*m+5 = 0

4*m+5 = 0

4*m+5 = 0 // - 5

4*m = -5 // : 4

m = -5/4

4*m^2-(3*m)-10 = 0

4*m^2-(3*m)-10 = 0

4*m^2-3*m-10 = 0

4*m^2-3*m-10 = 0

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

DELTA = 169

DELTA > 0

m = (169^(1/2)+3)/(2*4) or m = (3-169^(1/2))/(2*4)

m = 2 or m = -5/4

m in (-oo:-5/4) U (-5/4:2) U (2:+oo)

6/(4*m+5)-(6/(m-2)) = 1/(4*m^2-(3*m)-10) // - 1/(4*m^2-(3*m)-10)

6/(4*m+5)-(6/(m-2))-(1/(4*m^2-(3*m)-10)) = 0

6/(4*m+5)-6*(m-2)^-1-(4*m^2-3*m-10)^-1 = 0

6/(4*m+5)-6/(m-2)-1/(4*m^2-3*m-10) = 0

4*m^2-3*m-10 = 0

4*m^2-3*m-10 = 0

4*m^2-3*m-10 = 0

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

DELTA = 169

DELTA > 0

m = (169^(1/2)+3)/(2*4) or m = (3-169^(1/2))/(2*4)

m = 2 or m = -5/4

(m+5/4)*(m-2) = 0

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

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

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

-18*m^2-129/2*m-4*m-105/2-5 = 0

-18*m^2-137/2*m-115/2 = 0

-18*m^2-137/2*m-115/2 = 0

-1*(18*m^2+137/2*m+115/2) = 0

18*m^2+137/2*m+115/2 = 0

DELTA = (137/2)^2-(4*18*115/2)

DELTA = 2209/4

DELTA > 0

m = ((2209/4)^(1/2)-137/2)/(2*18) or m = (-(2209/4)^(1/2)-137/2)/(2*18)

m = -5/4 or m = -23/9

-1*(m+23/9)*(m+5/4) = 0

(-1*(m+23/9)*(m+5/4))/((4*m+5)*(m-2)*(m+5/4)) = 0

(-1*(m+23/9)*(m+5/4))/((4*m+5)*(m-2)*(m+5/4)) = 0 // * (4*m+5)*(m-2)*(m+5/4)

-1*(m+23/9)*(m+5/4) = 0

( m+23/9 )

m+23/9 = 0 // - 23/9

m = -23/9

( m+5/4 )

m+5/4 = 0 // - 5/4

m = -5/4

m in { -5/4} 

m = -23/9

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