Question

$\frac{1}{x} - \frac{1}{x - 2} = 0$
​

Answer 1

Answer:

Answer:

\begin{gathered}\frac{1}{x} - \frac{1}{x - 2} = 3 \\ take \: lcm \: \\ lcm \: (x \: and \: x - 2) = x(x - 2) \\ then \\ \frac{(x - 2) - x}{x(x - 2)} = 3 \\ by \: cross \: multiplication \\ x - 2 - x = 3x(x - 2) \\ - 2 = 3 {x}^{2} - 6x \\ 3 {x}^{2} - 6x + 2 = 0 \\ so \: x = \frac{ - (- 6 )\frac{ + }{} \sqrt{ {( - 6)}^{2} - 4(3)(2)} }{2 \times 3} \\ = \frac{6 \frac{ + }{} \sqrt{36 - 24} }{6} \\ = 1 \frac{ + }{} \frac{ \sqrt{12} }{6} \\ so \: x = 1 + \frac{ \sqrt{12} }{6} \\ or \: 1 - \frac{ \sqrt{12} }{6}\end{gathered}

x

1

−

x−2

1

=3

takelcm

lcm(xandx−2)=x(x−2)

then

x(x−2)

(x−2)−x

=3

bycrossmultiplication

x−2−x=3x(x−2)

−2=3x

2

−6x

3x

2

−6x+2=0

sox=

2×3

−(−6)

+

(−6)

2

−4(3)(2)

=

6

6

+

36−24

=1

+

6

12

sox=1+

6

12

or1−

6

12