(1/(X-5))+(1/(X-2))=7/10

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Solution for (1/(X-5))+(1/(X-2))=7/10 equation: 


D( X )

X-2 = 0

X-5 = 0

X-2 = 0

X-2 = 0

X-2 = 0 // + 2

X = 2

X-5 = 0

X-5 = 0

X-5 = 0 // + 5

X = 5

X in (-oo:2) U (2:5) U (5:+oo)

1/(X-5)+1/(X-2) = 7/10 // - 7/10

1/(X-5)+1/(X-2)-(7/10) = 0

1/(X-5)+1/(X-2)-7/10 = 0

(1*10*(X-2))/(10*(X-5)*(X-2))+(1*10*(X-5))/(10*(X-5)*(X-2))+(-7*(X-5)*(X-2))/(10*(X-5)*(X-2)) = 0

1*10*(X-2)+1*10*(X-5)-7*(X-5)*(X-2) = 0

20*X-7*X^2+49*X-70-70 = 0

69*X-7*X^2-140 = 0

69*X-7*X^2-140 = 0

69*X-7*X^2-140 = 0

DELTA = 69^2-(-140*(-7)*4)

DELTA = 841

DELTA > 0

X = (841^(1/2)-69)/(-7*2) or X = (-841^(1/2)-69)/(-7*2)

X = 20/7 or X = 7

(X-20/7)*(X-7) = 0

((X-20/7)*(X-7))/(10*(X-5)*(X-2)) = 0

((X-20/7)*(X-7))/(10*(X-5)*(X-2)) = 0 // * 10*(X-5)*(X-2)

(X-20/7)*(X-7) = 0

( X-20/7 )

X-20/7 = 0 // + 20/7

X = 20/7

( X-7 )

X-7 = 0 // + 7

X = 7

X in { 20/7, 7 }

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