Question

If `(x^2 - 4)/(x^2 + 4) = 3/5`, the value of x is ______.

Options

• 4

• ± 4

• `1/4`

• `± 1/4`

Answer 1

If `(x^2 - 4)/(x^2 + 4) = 3/5`, the value of x is ± 4.

Explanation:

Given `(x^2 - 4)/(x^2 + 4) = 3/5`

Applying componendo and dividendo,

`(x^2 - 4 + x^2 + 4)/(x^2 - 4 - (x^2 + 4)) = (3 + 5)/(3 - 5)`

`\implies (2x^2)/(x^2 - 4 - x^2 - 4) = 8/(-2)`

`\implies (2x^2)/-8 = -4`

`\implies 2x^2 = 32`

`\implies x^2 = 16`

`\implies x = ±sqrt(16)`

`\implies x = ± 4`