((x-5)/(4x^2-9))*((4x^2+12x+9)/(2x^2-11x+5))

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Solution for ((x-5)/(4x^2-9))*((4x^2+12x+9)/(2x^2-11x+5)) equation: 


D( x )

2*x^2-(11*x)+5 = 0

4*x^2-9 = 0

2*x^2-(11*x)+5 = 0

2*x^2-(11*x)+5 = 0

2*x^2-11*x+5 = 0

2*x^2-11*x+5 = 0

DELTA = (-11)^2-(2*4*5)

DELTA = 81

DELTA > 0

x = (81^(1/2)+11)/(2*2) or x = (11-81^(1/2))/(2*2)

x = 5 or x = 1/2

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 (-3/2:1/2) U (1/2:3/2) U (3/2:5) U (5:+oo)

((x-5)/(4*x^2-9))*((4*x^2+12*x+9)/(2*x^2-(11*x)+5)) = 0

((x-5)/(4*x^2-9))*((4*x^2+12*x+9)/(2*x^2-11*x+5)) = 0

((x-5)*(4*x^2+12*x+9))/((4*x^2-9)*(2*x^2-11*x+5)) = 0

4*x^2+12*x+9 = 0

4*x^2+12*x+9 = 0

DELTA = 12^2-(4*4*9)

DELTA = 0

x = -12/(2*4)

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

(x+3/2)^2 = 0

2*x^2-11*x+5 = 0

2*x^2-11*x+5 = 0

DELTA = (-11)^2-(2*4*5)

DELTA = 81

DELTA > 0

x = (81^(1/2)+11)/(2*2) or x = (11-81^(1/2))/(2*2)

x = 5 or x = 1/2

(x-1/2)*(x-5) = 0

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

( x+3/2 )

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

x = -3/2

( x-5 )

x-5 = 0 // + 5

x = 5

x in { -3/2} 

x in { 5} 

x belongs to the empty set

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