1/(x-5)+1/(x-4)=9/20

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Solution for 1/(x-5)+1/(x-4)=9/20 equation: 


D( x )

x-5 = 0

x-4 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:4) U (4:5) U (5:+oo)

1/(x-5)+1/(x-4) = 9/20 // - 9/20

1/(x-5)+1/(x-4)-(9/20) = 0

1/(x-5)+1/(x-4)-9/20 = 0

(1*20*(x-4))/(20*(x-5)*(x-4))+(1*20*(x-5))/(20*(x-5)*(x-4))+(-9*(x-5)*(x-4))/(20*(x-5)*(x-4)) = 0

1*20*(x-4)+1*20*(x-5)-9*(x-5)*(x-4) = 0

40*x-9*x^2+81*x-180-180 = 0

121*x-9*x^2-360 = 0

121*x-9*x^2-360 = 0

121*x-9*x^2-360 = 0

DELTA = 121^2-(-360*(-9)*4)

DELTA = 1681

DELTA > 0

x = (1681^(1/2)-121)/(-9*2) or x = (-1681^(1/2)-121)/(-9*2)

x = 40/9 or x = 9

(x-40/9)*(x-9) = 0

((x-40/9)*(x-9))/(20*(x-5)*(x-4)) = 0

((x-40/9)*(x-9))/(20*(x-5)*(x-4)) = 0 // * 20*(x-5)*(x-4)

(x-40/9)*(x-9) = 0

( x-40/9 )

x-40/9 = 0 // + 40/9

x = 40/9

( x-9 )

x-9 = 0 // + 9

x = 9

x in { 40/9, 9 }

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