(2x-2)/(4x^2-9)-(5)/(3-2x)

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Solution for (2x-2)/(4x^2-9)-(5)/(3-2x) equation: 


D( x )

3-(2*x) = 0

4*x^2-9 = 0

3-(2*x) = 0

3-(2*x) = 0

3-2*x = 0

3-2*x = 0 // - 3

-2*x = -3 // : -2

x = -3/(-2)

x = 3/2

4*x^2-9 = 0

4*x^2-9 = 0

4*x^2 = 9 // : 4

x^2 = 9/4

x^2 = 9/4 // ^ 1/2

abs(x) = 3/2

x = 3/2 or x = -3/2

x in (-oo:-3/2) U (-3/2:3/2) U (3/2:+oo)

(2*x-2)/(4*x^2-9)-(5/(3-(2*x))) = 0

(2*x-2)/(4*x^2-9)-5*(3-2*x)^-1 = 0

(2*x-2)/(4*x^2-9)-5/(3-2*x) = 0

((2*x-2)*(3-2*x))/((4*x^2-9)*(3-2*x))+(-5*(4*x^2-9))/((4*x^2-9)*(3-2*x)) = 0

(2*x-2)*(3-2*x)-5*(4*x^2-9) = 0

10*x-24*x^2+39 = 0

10*x-24*x^2+39 = 0

10*x-24*x^2+39 = 0

DELTA = 10^2-(-24*4*39)

DELTA = 3844

DELTA > 0

x = (3844^(1/2)-10)/(-24*2) or x = (-3844^(1/2)-10)/(-24*2)

x = -13/12 or x = 3/2

(x+13/12)*(x-3/2) = 0

((x+13/12)*(x-3/2))/((4*x^2-9)*(3-2*x)) = 0

((x+13/12)*(x-3/2))/((4*x^2-9)*(3-2*x)) = 0 // * (4*x^2-9)*(3-2*x)

(x+13/12)*(x-3/2) = 0

( x+13/12 )

x+13/12 = 0 // - 13/12

x = -13/12

( x-3/2 )

x-3/2 = 0 // + 3/2

x = 3/2

x in { 3/2} 

x = -13/12

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