Answer:

Solution

x

1 −

x−2

1

=3

⇒3x(x−2)=x−2−x

⇒3x

2

−6x+2=0

⇒9x

2

−18x+6=0

⇒(3x)

2

−2(3x)(3)+3

2

−3=0

⇒(3x−3)

2

=3

⇒3x−3=±

3

⇒x=

3

3±

3

⇒x=1±

3

1

⇒x=1+

3

1

or

x=1−

3

1

Verified answer

Step-by-step explanation:

1/x - 1/(x-2) = 3

{x-2-(x)}/x(x-2) = 3

(x-2-x)/(x²-2x) = 3

-2/(x²-2x) =3

-2 = 3(x²-2x)

-2= 3x²-6x

3x²-6x+2=0

D= b²-4ac

D= (-6)²-4•3•2

D= 36-24

D= 12

√D= √12

√D= 2√3

x= (-b±√D)/2a

x= {-(-6)±2√3)/2×3

x= (6±2√3)/6

x= 2(3±√3)/6

x= (3±√3)/3

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