((3x-21)/6x-6)*((x^2-1)/(x^2-49))

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Solution for ((3x-21)/6x-6)*((x^2-1)/(x^2-49)) equation: 


D( x )

x^2-49 = 0

x^2-49 = 0

x^2-49 = 0

1*x^2 = 49 // : 1

x^2 = 49

x^2 = 49 // ^ 1/2

abs(x) = 7

x = 7 or x = -7

x in (-oo:-7) U (-7:7) U (7:+oo)

(x*((3*x-21)/6)-6)*((x^2-1)/(x^2-49)) = 0

((x^2-1)*((x*(3*x-21))/6-6))/(x^2-49) = 0

(x*(3*x-21))/6-6 = 0

(x*(3*x-21))/6+(-6*6)/6 = 0

x*(3*x-21)-6*6 = 0

3*x^2-21*x-36 = 0

3*x^2-21*x-36 = 0

3*(x^2-7*x-12) = 0

x^2-7*x-12 = 0

DELTA = (-7)^2-(-12*1*4)

DELTA = 97

DELTA > 0

x = (97^(1/2)+7)/(1*2) or x = (7-97^(1/2))/(1*2)

x = (97^(1/2)+7)/2 or x = (7-97^(1/2))/2

3*(x-((7-97^(1/2))/2))*(x-((97^(1/2)+7)/2)) = 0

(3*(x-((7-97^(1/2))/2))*(x-((97^(1/2)+7)/2)))/6 = 0

(3*(x-((7-97^(1/2))/2))*(x-((97^(1/2)+7)/2)))/6 = 0 // * 6

3*(x-((7-97^(1/2))/2))*(x-((97^(1/2)+7)/2)) = 0

(3*(x^2-1)*(x-((7-97^(1/2))/2))*(x-((97^(1/2)+7)/2)))/(x^2-49) = 0

( x-((7-97^(1/2))/2) )

x-((7-97^(1/2))/2) = 0 // + (7-97^(1/2))/2

x = (7-97^(1/2))/2

( x-((97^(1/2)+7)/2) )

x-((97^(1/2)+7)/2) = 0 // + (97^(1/2)+7)/2

x = (97^(1/2)+7)/2

( x^2-1 )

1*x^2 = 1 // : 1

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

x in { (7-97^(1/2))/2, (97^(1/2)+7)/2, 1, -1 }

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