Question

(x²+x+1)² ÷ x²-x+1 me ajuda pfvr ​

Answer 1

Olá!

(x² + x + 1)² ÷ x² - x + 1 =

($(x^{2} )^{2}$ + $x^{2}$ + $1^{2}$ + 2x² · x + 2x² · 1 + 2x · 1) ÷ x² - x + 1 =

($x^{4}$ + $x^{2}$ + 1 + 2x³ + 2x + 2x) ÷ x² - x + 1 =

($x^{4}$ + 2x³ + 4x + 1) ÷ x² - x + 1 =

x² + 2x + $4x^{-1}$ + $\frac{1}{x^{2} }$ - x + 1 =

x² + 2x + $\frac{4}{x}$ + $\frac{1}{x^{2} }$ - x + 1 =

x² + x + $\frac{4}{x}$ + $\frac{1}{x^{2} }$ + 1 =

$\frac{x^{2} x^{2} }{x^{2} }$ + $\frac{x^{2} x}{x^{2} }$ + $\frac{4x}{x^{2} }$ + $\frac{x^{2} }{x^{2} }$ =

x²x² + x²x + 4x + x² =

$x^{4}$ + $x^{3}$ + x² + 4x

Abraços!