Question

The decimal expansion of the rational no. X-1/2x+1. +x-1/2x+1 =2 will terminate after how many digits

Answer 1

The value of x is equal to - 2.

Step-by-step explanation:

Given,

The decimal expansion of the rational number:

$\dfrac{x-1}{2x+1} +\dfrac{x-1}{2x+1} =2$

To find, the value of x = ?

∴ $\dfrac{x-1}{2x+1} +\dfrac{x-1}{2x+1} =2$

⇒ $\dfrac{x-1+x-1}{2x+1} =2$

⇒ $\dfrac{2x-2}{2x+1} =2$

⇒ $\dfrac{2(x-1)}{2x+1} =2$

⇒ x - 1 = 2x + 1

⇒ 2x - x = - 1 - 1

⇒ x = - 2

Thus, the value of x is equal to - 2.