3x/(x^2-10x+25)+4x/(x^2-x-20)

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Solution for 3x/(x^2-10x+25)+4x/(x^2-x-20) equation:


D( x )

x^2-x-20 = 0

x^2-(10*x)+25 = 0

x^2-x-20 = 0

x^2-x-20 = 0

x^2-x-20 = 0

DELTA = (-1)^2-(-20*1*4)

DELTA = 81

DELTA > 0

x = (81^(1/2)+1)/(1*2) or x = (1-81^(1/2))/(1*2)

x = 5 or x = -4

x^2-(10*x)+25 = 0

x^2-(10*x)+25 = 0

x^2-10*x+25 = 0

x^2-10*x+25 = 0

DELTA = (-10)^2-(1*4*25)

DELTA = 0

x = 10/(1*2)

x = 5 or x = 5

x in (-oo:-4) U (-4:5) U (5:+oo)

(3*x)/(x^2-(10*x)+25)+(4*x)/(x^2-x-20) = 0

(3*x)/(x^2-10*x+25)+(4*x)/(x^2-x-20) = 0

x^2-10*x+25 = 0

x^2-10*x+25 = 0

x^2-10*x+25 = 0

DELTA = (-10)^2-(1*4*25)

DELTA = 0

x = 10/(1*2)

x = 5 or x = 5

(x-5)^2 = 0

x^2-x-20 = 0

x^2-x-20 = 0

x^2-x-20 = 0

DELTA = (-1)^2-(-20*1*4)

DELTA = 81

DELTA > 0

x = (81^(1/2)+1)/(1*2) or x = (1-81^(1/2))/(1*2)

x = 5 or x = -4

(x+4)*(x-5) = 0

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

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

3*x*(x+4)+4*x*(x-5) = 0

7*x^2-8*x = 0

7*x^2-8*x = 0

x*(7*x-8) = 0

7*x-8 = 0 // + 8

7*x = 8 // : 7

x = 8/7

x*(x-8/7) = 0

(x*(x-8/7))/((x-5)^2*(x+4)) = 0

(x*(x-8/7))/((x-5)^2*(x+4)) = 0 // * (x-5)^2*(x+4)

x*(x-8/7) = 0

( x-8/7 )

x-8/7 = 0 // + 8/7

x = 8/7

( x )

x = 0

x in { 8/7, 0 }

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