Question

Please solve this question neatly!

Answer 1

$Given : (\frac{x + 1}{x})(\frac{x^2 + 1}{x^2})(\frac{x - 1}{x})(\frac{x^4 + 1}{x^4})$

$= > \frac{(x + 1)(x^2 + 1)(x - 1)(x^4 + 1)}{x(x^2)(x)(x^4)}$

$= > \frac{(x + 1)(x^2 + 1)(x - 1)(x^4 + 1)}{x^8}$

$= > \frac{(x * x^2 + x * 1 + 1 * x^2 + 1 * 1)(x - 1)(x^4 + 1)}{x^8}$

$= > \frac{(x^3 + x + x^2 + 1)(x - 1)(x^4 + 1)}{x^8}$

$= > \frac{(x^3 * x - x^3 * 1 + x * x - x * 1 + x^2 * x - x^2 + 1 * x - 1 * 1)(x^4 + 1)}{x^8}$

$= > \frac{(x^4 - x^3 + x^2 - x + x^3 - x^2 + x - 1)(x^4 + 1)}{x^8}$

$= > \frac{(x^4 - 1)(x^4 + 1)}{x^8}$

$= > \frac{x^8 - 1}{x^8}$

Hope this helps!