Ensino Médio ⇒ (UFF - 2018) Simplificação Tópico resolvido

[edinaldoprof]

Simplifique:

a) [tex3]\frac{x^{6}-x^{2}}{x^{2}-2x+1}[/tex3], x [tex3]\neq [/tex3] 1;

b) [tex3]\frac{3x^{2}-21x+36}{3x^{2}-27}[/tex3], x [tex3]\neq \pm [/tex3] 3.

[edinaldoprof]

@edinaldoprof,

a) [tex3]Numerador:(x^6 - x^2) \implies x^2(x^4 - 1) \implies x^2(x^2 - 1)(x^2 + 1) \implies x^2(x - 1)(x + 1)(x^2 + 1).[/tex3]
[tex3]Denominador: x^2 - 2x + 1 = (x - 1)^2\\
\frac{x^2(\cancel{x - 1})(x + 1)(x^2 + 1)}{(x - 1)\cancel{^2}} \implies \boxed{\mathbf{\frac{x^2(x + 1)(x^2 + 1)}{x - 1}}}
[/tex3]
b)[tex3] Numerador: 3x^2 - 21x + 36 \implies 3(x^2 - 7x + 12) \implies 3(x - 3)(x - 4)[/tex3]
[tex3]Denominador: 3x^2 - 27 \implies 3(x^2 - 9) \implies 3(x - 3)(x + 3)\\
\frac{\cancel{3(x - 3)}(x - 4)}{\cancel{3(x - 3)}(x + 3)} \implies\boxed{\mathbf{\frac{x - 4}{x + 3}}}[/tex3]