(x^2-25)/(x^3-5x^2-7x+35)

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Solution for (x^2-25)/(x^3-5x^2-7x+35) equation: 


D( x )

x^3-(5*x^2)-(7*x)+35 = 0

x^3-(5*x^2)-(7*x)+35 = 0

x^3-(5*x^2)-(7*x)+35 = 0

x^3-5*x^2-7*x+35 = 0

x^3-5*x^2-7*x+35 = 0

{ 1, -1, 5, -5, 7, -7, 35, -35 }

1

x = 1

x^3-5*x^2-7*x+35 = 24

1

-1

x = -1

x^3-5*x^2-7*x+35 = 36

-1

5

x = 5

x^3-5*x^2-7*x+35 = 0

5

x-5

x^2-7

x^3-5*x^2-7*x+35

x-5

5*x^2-x^3

35-7*x

7*x-35

0

x^2-7 = 0

DELTA = 0^2-(-7*1*4)

DELTA = 28

DELTA > 0

x = (28^(1/2)+0)/(1*2) or x = (0-28^(1/2))/(1*2)

x = 7^(1/2) or x = -7^(1/2)

x in { -7^(1/2), 7^(1/2), 5} 

x in (-oo:-7^(1/2)) U (-7^(1/2):7^(1/2)) U (7^(1/2):5) U (5:+oo)

(x^2-25)/(x^3-(5*x^2)-(7*x)+35) = 0

(x^2-25)/(x^3-5*x^2-7*x+35) = 0

x^3-5*x^2-7*x+35 = 0

x^3-5*x^2-7*x+35 = 0

{ 1, -1, 5, -5, 7, -7, 35, -35 }

1

x = 1

x^3-5*x^2-7*x+35 = 24

1

-1

x = -1

x^3-5*x^2-7*x+35 = 36

-1

5

x = 5

x^3-5*x^2-7*x+35 = 0

5

x-5

x^2-7

x^3-5*x^2-7*x+35

x-5

5*x^2-x^3

35-7*x

7*x-35

0

x^2-7 = 0

DELTA = 0^2-(-7*1*4)

DELTA = 28

DELTA > 0

x = (28^(1/2)+0)/(1*2) or x = (0-28^(1/2))/(1*2)

x = 7^(1/2) or x = -7^(1/2)

x in { -7^(1/2), 7^(1/2), 5} 

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

(x^2-25)/((x+7^(1/2))*(x-7^(1/2))*(x-5)) = 0

1*x^2 = 25 // : 1

x^2 = 25

x^2 = 25 // ^ 1/2

abs(x) = 5

x = 5 or x = -5

x in { 5} 

x = -5

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