((8x^3)+(-2x^2)+(-7x)+(3))/((4x)+(-3))

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Solution for ((8x^3)+(-2x^2)+(-7x)+(3))/((4x)+(-3)) equation: 


D( x )

4*x-3 = 0

4*x-3 = 0

4*x-3 = 0

4*x-3 = 0 // + 3

4*x = 3 // : 4

x = 3/4

x in (-oo:3/4) U (3/4:+oo)

(8*x^3-2*x^2-7*x+3)/(4*x-3) = 0

8*x^3-2*x^2-7*x+3 = 0

8*x^3-2*x^2-7*x+3 = 0

{ 1, -1, 3, -3 }

1

x = 1

8*x^3-2*x^2-7*x+3 = 2

1

-1

x = -1

8*x^3-2*x^2-7*x+3 = 0

-1

x+1

8*x^2-10*x+3

8*x^3-2*x^2-7*x+3

x+1

-8*x^3-8*x^2

3-10*x^2-7*x

10*x^2+10*x

3*x+3

-3*x-3

0

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

DELTA = (-10)^2-(3*4*8)

DELTA = 4

DELTA > 0

x = (4^(1/2)+10)/(2*8) or x = (10-4^(1/2))/(2*8)

x = 3/4 or x = 1/2

x in { 1/2, 3/4, -1} 

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

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x-1/2 )

x-1/2 = 0 // + 1/2

x = 1/2

( x-3/4 )

x-3/4 = 0 // + 3/4

x = 3/4

x in { 3/4} 

x in { -1, 1/2 }

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