Question

one upon x minus one upon x minus 2 is equal to 3 X is not equal to 0, 2​

Answer 1

Step-by-step explanation:

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

3x=0-2

3x=-2

x=-2/3

Answer 2

$x= \frac{-3- 2\sqrt{3}}{6}, x= \frac{-3+ 2\sqrt{3}}{6}$

Step-by-step explanation:

given :

$\frac{1}{x}-\frac{1}{x-2}=3$

solving

$\frac{1}{x}-\frac{1}{x-2}=3 \\\\\frac{x-2-x}{x(x-2)}=3 \\\\\frac{-2}{x^2-2x}=3\\\\-2=3x^2-6x\\\\3x^2-6x+2=0\\\\ax^2+bx+c=0\\\\a=3,b=-6,c=2\\\\D = b^2-4ac \\\\D = (-6)^2-4\times 3\times 2\\\\D= 36-24 = 12$

therefore D = 12

now ,

roots are :

$x= \frac{-b \pm \sqrt{D}}{2a}\\\\x= \frac{-3\pm \sqrt{12}}{6}\\\\x= \frac{-3\pm 2\sqrt{3}}{6}\\\\x= \frac{-3- 2\sqrt{3}}{6}, x= \frac{-3+ 2\sqrt{3}}{6}$

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