Question

Me ajudem, por favor!
Simplifique as expressões em cada caso:

Answer 1

Resposta:

a) 12/5

b) 7/4

c) p - 1

d)

$\frac{(xy)^{2}}{y^{2}+x^{2} }$

Explicação passo-a-passo:

Para simplificar as expressoes voce precisa colocar em evidencia o fator que quer cancelar, geralmente o fator com a letra.

a)

$\frac{3^{n+2}-3^{n}}{3^{n+1}+3^{n-1}  }\\\\\frac{3^{n} (3^{2} - 3^{0})}{3^{n}(3^{1} + 3^{-1})}\\\\\frac{9-1}{3+\frac{1}{3}}\\\\\frac{8}{\frac{9+1}{3}}\\\\\frac{8}{\frac{10}{3}}\\\\\frac{8}{1}*\frac{3}{10}\\\\\frac{24}{10}\\\\\frac{12}{5}$

b)

$\frac{2^{n+1}-2^{n-2}}{2^{n}}\\\\\frac{2^{n}(2^{1}-2^{-2})}{2^{n}}\\\\2-\frac{1}{4}\\\\\frac{8-1}{4}\\\\\frac{7}{4}$

c)

$\frac{p^{2n+1 - p^{2n}}}{p^{2n}}\\\\\frac{p^{2n}(p^{1}-p^{0})}{p^{2n}}\\\\p - 1$

d)

$(x^{-2} + y^{-2})^{-1}\\\\\frac{1}{x^{-2} + y^{-2}}\\\\\frac{1}{\frac{1}{x^{2}} +\frac{1}{y^{2}}}\\\\\frac{1}{\frac{y^{2} + x^{2}}{(xy)^{2}}}\\\\\frac{1}{1}*\frac{(xy)^{2}}{y^{2}+x^{2}}\\\\\frac{(xy)^{2}}{y^{2}+x^{2} }$