Question

solve1/x+1/x+1-2/x-1=0​

Answer 1

Step-by-step explanation:

$\frac{1}{x} + \frac{1}{x + 1} - \frac{2}{x - 1} = 0$

⇒$\frac{(x - 1)^{2} + x(x - 1) - 2x(x - 1)}{x(x - 1)^{2} } = 0$

⇒${x}^{2} + 1 - 2x + {x}^{2} - x - {2x}^{2} + 2 = 0$

⇒$- 3x + 3 = 0$

⇒$- 3x = - 3$

⇒$x = \frac{3}{3} = 1$

⇒$x = 1$

Answer 2

Answer:

x

1

+

x+1

1

−

x−1

2

=0

⇒\frac{(x - 1)^{2} + x(x - 1) - 2x(x - 1)}{x(x - 1)^{2} } = 0

x(x−1)

2

(x−1)

2

+x(x−1)−2x(x−1)

=0

⇒{x}^{2} + 1 - 2x + {x}^{2} - x - {2x}^{2} + 2 = 0x

2

+1−2x+x

2

−x−2x

2

+2=0

⇒- 3x + 3 = 0−3x+3=0

⇒- 3x = - 3−3x=−3

⇒x = \frac{3}{3} = 1x=

3

3

=1

⇒x = 1x=1