Question

If `(x^2 - 1)/(x^2 + 1) = 3/5`, the value of x is ______.

Options

• `1/2`

• 2

• `± 1/2`

• ±2

Answer 1

If `(x^2 - 1)/(x^2 + 1) = 3/5`, the value of x is ±2.

Explanation:

Given `(x^2 - 1)/(x^2 + 1) = 3/5`

`\implies` 5(x² – 1) = 3(x² + 1)

`\implies` 5x² – 5 = 3x² + 3

`\implies` 5x² – 3x² = 3 + 5

`\implies` 2x² = 8

`\implies` x² = 4

`\implies` x = `±sqrt(4)` 

`\implies` x = ±2