(2x-5)/x=(x-2)/3

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Solution for (2x-5)/x=(x-2)/3 equation:


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

(2*x-5)/x = (x-2)/3 // - (x-2)/3

(2*x-5)/x-((x-2)/3) = 0

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

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

3*(2*x-5)-1*x*(x-2) = 0

8*x-x^2-15 = 0

8*x-x^2-15 = 0

8*x-x^2-15 = 0

DELTA = 8^2-(-15*(-1)*4)

DELTA = 4

DELTA > 0

x = (4^(1/2)-8)/(-1*2) or x = (-4^(1/2)-8)/(-1*2)

x = 3 or x = 5

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

((x-3)*(x-5))/(3*x) = 0

((x-3)*(x-5))/(3*x) = 0 // * 3*x

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

( x-3 )

x-3 = 0 // + 3

x = 3

( x-5 )

x-5 = 0 // + 5

x = 5

x in { 3, 5 }

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