Question

Solve 1/x-1/x-2=3,x≠0,2

Answer 1

Answer:

$x =\frac{3±\sqrt{3}}{3}$

Step-by-step explanation:

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

$\implies \frac{x-2-x}{x(x-2)}=3$

$\implies -2=3x(x-2)$

$\implies 0=3x^{2}-6x+2$

$\implies 3x^{2}-6x+2=0$

/* Compare this with ax²+bx+c=0 , we get,

a = 3, b = -6, c = 2

Discreminant (D) = b²-4ac

= (-6)²-4×3×2

= 36-24

= 12

√D = √12 = 2√3

By Quadratic Formula:

$x = \frac{-b±\sqrt{D}}{2a}\\= \frac{-(-6)±2\sqrt{3}}{2\times 3}\\=\frac{6±2\sqrt{3}}{6}\\=\frac{2(3±\sqrt{3})}{6}\\=\frac{3±\sqrt{3}}{3}$

Therefore,.

$x =\frac{3±\sqrt{3}}{3}$

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