8x-1/(x-2)*(x+3)

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Solution for 8x-1/(x-2)*(x+3) 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)

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

8*x-((x-2)^-1*(x+3)) = 0

(-1*(x+3))/(x-2)+8*x = 0

(-1*(x+3))/(x-2)+(8*x*(x-2))/(x-2) = 0

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

8*x^2-17*x-3 = 0

8*x^2-17*x-3 = 0

8*x^2-17*x-3 = 0

DELTA = (-17)^2-(-3*4*8)

DELTA = 385

DELTA > 0

x = (385^(1/2)+17)/(2*8) or x = (17-385^(1/2))/(2*8)

x = (385^(1/2)+17)/16 or x = (17-385^(1/2))/16

(x-((17-385^(1/2))/16))*(x-((385^(1/2)+17)/16)) = 0

((x-((17-385^(1/2))/16))*(x-((385^(1/2)+17)/16)))/(x-2) = 0

((x-((17-385^(1/2))/16))*(x-((385^(1/2)+17)/16)))/(x-2) = 0 // * x-2

(x-((17-385^(1/2))/16))*(x-((385^(1/2)+17)/16)) = 0

( x-((17-385^(1/2))/16) )

x-((17-385^(1/2))/16) = 0 // + (17-385^(1/2))/16

x = (17-385^(1/2))/16

( x-((385^(1/2)+17)/16) )

x-((385^(1/2)+17)/16) = 0 // + (385^(1/2)+17)/16

x = (385^(1/2)+17)/16

x in { (17-385^(1/2))/16, (385^(1/2)+17)/16 }

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