2/(x^2-6x+8)=1/(x-4)-1/(x-2)

Question

2/(x^2-6x+8)=1/(x-4)-1/(x-2)

Answer 1

1/( Х - 4 ) - 1/( Х - 2 ) = ( Х - 2 - ( Х - 4 )) / ( ( Х - 4 )( Х - 2 )) = ( Х - 2 - Х + 4 ) / ( ( х - 4 )( х - 2 )) = 2 / ( ( х - 4 )( х - 2 ))
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Х^2 - 6х + 8 = ( x - 4 )( x - 2 )
D = 36 - 32 = 4 = 2^2
X1 = ( 6 + 2 ) : 2 = 4
X2 = ( 6 - 2 ) : 2 = 2
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2 /( ( x - 4 )( x - 2 )) = 2 / (( x - 4 )( x - 2 ))