Question

Wykonaj działanie:

(x² + ¹/x) / (x + ¹/x - 1) : (x² - ¹/x) / (x + ¹/x + 1) =

Załączam graficzną wersję.

Answer 1

(x² + ¹/x) / (x + ¹/x - 1) : (x² - ¹/x) / (x + ¹/x + 1) =

 

Z:

 

x ∈ R \ { 0, 1}

 

 

(x² + ¹/x) / (x + ¹/x - 1) : (x² - ¹/x) / (x + ¹/x + 1) =

 

= {[(x³ + 1)/x)] / [(x² - x + 1)/x]} : {[(x³ - 1)/x] / [(x² + x + 1)/x]} =

 

= [(x³ + 1)/(x² - x + 1)] : [(x³ - 1)/(x² + x + 1)] =

 

= [(x + 1)*(x² - x + 1)/(x² - x + 1)] : [(x - 1)*(x² + x + 1)/(x² + x + 1)] =

 

= (x + 1)/(x - 1)