((2x^2+x-3)/(4x^2-9))((7x^2-7x)/(5x-5))

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Solution for ((2x^2+x-3)/(4x^2-9))((7x^2-7x)/(5x-5)) equation: 


D( x )

4*x^2-9 = 0

5*x-5 = 0

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

5*x-5 = 0

5*x-5 = 0

5*x-5 = 0 // + 5

5*x = 5 // : 5

x = 5/5

x = 1

x in (-oo:-3/2) U (-3/2:1) U (1:3/2) U (3/2:+oo)

((2*x^2+x-3)/(4*x^2-9))*((7*x^2-(7*x))/(5*x-5)) = 0

((2*x^2+x-3)/(4*x^2-9))*((7*x^2-7*x)/(5*x-5)) = 0

((2*x^2+x-3)*(7*x^2-7*x))/((4*x^2-9)*(5*x-5)) = 0

2*x^2+x-3 = 0

2*x^2+x-3 = 0

DELTA = 1^2-(-3*2*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)-1)/(2*2) or x = (-25^(1/2)-1)/(2*2)

x = 1 or x = -3/2

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

7*x^2-7*x = 0

7*x*(x-1) = 0

x-1 = 0 // + 1

x = 1

7*x*(x-1) = 0

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

( 7*x )

7*x = 0 // : 7

x = 0

( x+3/2 )

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

x = -3/2

( x-1 )

x-1 = 0 // + 1

x = 1

x in { -3/2} 

x in { 1} 

x = 0

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