5/(x+2)+3/2(x+2)=1/(x+2)+22

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Solution for 5/(x+2)+3/2(x+2)=1/(x+2)+22 equation: 


D( x )

x+2 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x in (-oo:-2) U (-2:+oo)

5/(x+2)+(3/2)*(x+2) = 1/(x+2)+22 // - 1/(x+2)+22

5/(x+2)+(3/2)*(x+2)-(1/(x+2))-22 = 0

5/(x+2)+(3/2)*(x+2)-(x+2)^-1-22 = 0

5/(x+2)+3/2*(x+2)-1/(x+2)-22 = 0

5/(x+2)+(3/2*(x+2)^2)/(x+2)-1/(x+2)+(-22*(x+2))/(x+2) = 0

3/2*(x+2)^2-22*(x+2)-1+5 = 0

3/2*x^2+6*x-22*x-44-1+11 = 0

3/2*x^2+6*x-22*x-44+10 = 0

3/2*x^2-16*x-34 = 0

3/2*x^2-16*x-34 = 0

3/2*x^2-16*x-34 = 0

DELTA = (-16)^2-(-34*3/2*4)

DELTA = 460

DELTA > 0

x = (460^(1/2)+16)/(3/2*2) or x = (16-460^(1/2))/(3/2*2)

x = (2*115^(1/2)+16)/3 or x = (16-2*115^(1/2))/3

(x-((16-2*115^(1/2))/3))*(x-((2*115^(1/2)+16)/3)) = 0

((x-((16-2*115^(1/2))/3))*(x-((2*115^(1/2)+16)/3)))/(x+2) = 0

((x-((16-2*115^(1/2))/3))*(x-((2*115^(1/2)+16)/3)))/(x+2) = 0 // * x+2

(x-((16-2*115^(1/2))/3))*(x-((2*115^(1/2)+16)/3)) = 0

( x-((16-2*115^(1/2))/3) )

x-((16-2*115^(1/2))/3) = 0 // + (16-2*115^(1/2))/3

x = (16-2*115^(1/2))/3

( x-((2*115^(1/2)+16)/3) )

x-((2*115^(1/2)+16)/3) = 0 // + (2*115^(1/2)+16)/3

x = (2*115^(1/2)+16)/3

x in { (16-2*115^(1/2))/3, (2*115^(1/2)+16)/3 }

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