(2x-9)/(x-7)+x/2=5/(x-7)

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Solution for (2x-9)/(x-7)+x/2=5/(x-7) equation:


D( x )

x-7 = 0

x-7 = 0

x-7 = 0

x-7 = 0 // + 7

x = 7

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

(2*x-9)/(x-7)+x/2 = 5/(x-7) // - 5/(x-7)

(2*x-9)/(x-7)-(5/(x-7))+x/2 = 0

(2*x-9)/(x-7)-5*(x-7)^-1+x/2 = 0

(2*x-9)/(x-7)-5/(x-7)+x/2 = 0

(2*(2*x-9))/(2*(x-7))+(-5*2)/(2*(x-7))+(x*(x-7))/(2*(x-7)) = 0

2*(2*x-9)+x*(x-7)-5*2 = 0

x^2+4*x-7*x-28 = 0

x^2-3*x-28 = 0

x^2-3*x-28 = 0

x^2-3*x-28 = 0

DELTA = (-3)^2-(-28*1*4)

DELTA = 121

DELTA > 0

x = (121^(1/2)+3)/(1*2) or x = (3-121^(1/2))/(1*2)

x = 7 or x = -4

(x+4)*(x-7) = 0

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

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

(x+4)*(x-7) = 0

( x+4 )

x+4 = 0 // - 4

x = -4

( x-7 )

x-7 = 0 // + 7

x = 7

x in { 7}

x = -4

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