((2x-5)/(4x+9))-((5x-2)/(5x-6))

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Solution for ((2x-5)/(4x+9))-((5x-2)/(5x-6)) equation:


D( x )

5*x-6 = 0

4*x+9 = 0

5*x-6 = 0

5*x-6 = 0

5*x-6 = 0 // + 6

5*x = 6 // : 5

x = 6/5

4*x+9 = 0

4*x+9 = 0

4*x+9 = 0 // - 9

4*x = -9 // : 4

x = -9/4

x in (-oo:-9/4) U (-9/4:6/5) U (6/5:+oo)

(2*x-5)/(4*x+9)-((5*x-2)/(5*x-6)) = 0

(2*x-5)/(4*x+9)+(-1*(5*x-2))/(5*x-6) = 0

((2*x-5)*(5*x-6))/((4*x+9)*(5*x-6))+(-1*(5*x-2)*(4*x+9))/((4*x+9)*(5*x-6)) = 0

(2*x-5)*(5*x-6)-1*(5*x-2)*(4*x+9) = 0

48-10*x^2-74*x = 0

48-10*x^2-74*x = 0

2*(24-5*x^2-37*x) = 0

24-5*x^2-37*x = 0

DELTA = (-37)^2-(-5*4*24)

DELTA = 1849

DELTA > 0

x = (1849^(1/2)+37)/(-5*2) or x = (37-1849^(1/2))/(-5*2)

x = -8 or x = 3/5

2*(x+8)*(x-3/5) = 0

(2*(x+8)*(x-3/5))/((4*x+9)*(5*x-6)) = 0

(2*(x+8)*(x-3/5))/((4*x+9)*(5*x-6)) = 0 // * (4*x+9)*(5*x-6)

2*(x+8)*(x-3/5) = 0

( x+8 )

x+8 = 0 // - 8

x = -8

( x-3/5 )

x-3/5 = 0 // + 3/5

x = 3/5

x in { -8, 3/5 }

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