7/(y^2-4)-4/(y-2)=5/(y-2)

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Solution for 7/(y^2-4)-4/(y-2)=5/(y-2) equation: 


D( y )

y^2-4 = 0

y-2 = 0

y^2-4 = 0

y^2-4 = 0

1*y^2 = 4 // : 1

y^2 = 4

y^2 = 4 // ^ 1/2

abs(y) = 2

y = 2 or y = -2

y-2 = 0

y-2 = 0

y-2 = 0 // + 2

y = 2

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

7/(y^2-4)-(4/(y-2)) = 5/(y-2) // - 5/(y-2)

7/(y^2-4)-(4/(y-2))-(5/(y-2)) = 0

7/(y^2-4)-4*(y-2)^-1-5*(y-2)^-1 = 0

7/(y^2-4)-4/(y-2)-5/(y-2) = 0

(7*(y-2))/((y^2-4)*(y-2))+(-4*(y^2-4))/((y^2-4)*(y-2))+(-5*(y^2-4))/((y^2-4)*(y-2)) = 0

7*(y-2)-4*(y^2-4)-5*(y^2-4) = 0

7*y-4*y^2-5*y^2+2+20 = 0

7*y-9*y^2+22 = 0

7*y-9*y^2+22 = 0

7*y-9*y^2+22 = 0

DELTA = 7^2-(-9*4*22)

DELTA = 841

DELTA > 0

y = (841^(1/2)-7)/(-9*2) or y = (-841^(1/2)-7)/(-9*2)

y = -11/9 or y = 2

(y+11/9)*(y-2) = 0

((y+11/9)*(y-2))/((y^2-4)*(y-2)) = 0

((y+11/9)*(y-2))/((y^2-4)*(y-2)) = 0 // * (y^2-4)*(y-2)

(y+11/9)*(y-2) = 0

( y+11/9 )

y+11/9 = 0 // - 11/9

y = -11/9

( y-2 )

y-2 = 0 // + 2

y = 2

y in { 2} 

y = -11/9

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