(8/(4-x))+(x/(5x-20))

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Solution for (8/(4-x))+(x/(5x-20)) equation: 


D( x )

5*x-20 = 0

4-x = 0

5*x-20 = 0

5*x-20 = 0

5*x-20 = 0 // + 20

5*x = 20 // : 5

x = 20/5

x = 4

4-x = 0

4-x = 0

4-x = 0 // - 4

-x = -4 // * -1

x = 4

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

8/(4-x)+x/(5*x-20) = 0

(8*(5*x-20))/((4-x)*(5*x-20))+(x*(4-x))/((4-x)*(5*x-20)) = 0

8*(5*x-20)+x*(4-x) = 0

44*x-x^2-160 = 0

44*x-x^2-160 = 0

44*x-x^2-160 = 0

DELTA = 44^2-(-160*(-1)*4)

DELTA = 1296

DELTA > 0

x = (1296^(1/2)-44)/(-1*2) or x = (-1296^(1/2)-44)/(-1*2)

x = 4 or x = 40

(x-4)*(x-40) = 0

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

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

(x-4)*(x-40) = 0

( x-40 )

x-40 = 0 // + 40

x = 40

( x-4 )

x-4 = 0 // + 4

x = 4

x in { 4} 

x = 40

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