((a+4)/(a-2)-3)=a/4

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Solution for ((a+4)/(a-2)-3)=a/4 equation:


D( a )

a-2 = 0

a-2 = 0

a-2 = 0

a-2 = 0 // + 2

a = 2

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

(a+4)/(a-2)-3 = a/4 // - a/4

(a+4)/(a-2)-(a/4)-3 = 0

(a+4)/(a-2)-a/4-3 = 0

(4*(a+4))/(4*(a-2))+(-a*(a-2))/(4*(a-2))+(-3*4*(a-2))/(4*(a-2)) = 0

4*(a+4)-a*(a-2)-3*4*(a-2) = 0

6*a-a^2-12*a+16+24 = 0

40-a^2-6*a = 0

40-a^2-6*a = 0

40-a^2-6*a = 0

DELTA = (-6)^2-(-1*4*40)

DELTA = 196

DELTA > 0

a = (196^(1/2)+6)/(-1*2) or a = (6-196^(1/2))/(-1*2)

a = -10 or a = 4

(a+10)*(a-4) = 0

((a+10)*(a-4))/(4*(a-2)) = 0

((a+10)*(a-4))/(4*(a-2)) = 0 // * 4*(a-2)

(a+10)*(a-4) = 0

( a+10 )

a+10 = 0 // - 10

a = -10

( a-4 )

a-4 = 0 // + 4

a = 4

a in { -10, 4 }

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