Question

a) Escreva a expressão a⁻²+(b⁻²a²+3a²b⁻²)⁻¹ na forma mais simples possível para a ≠ 0 e b ≠ 0

Answer 1

Bom dia!

$\frac{1}{a^2}+\frac{1}{\frac{a^2}{b^2}+3\frac{a^3}{b^2}}\\\frac{1}{a^2}+\frac{1}{\frac{4a^2}{b^2}}\\\frac{1}{a^2}+\frac{b^2}{4a^2}=\frac{4+b^2}{4a^2}$

Espero ter ajudado!

Answer 2

$a^-^2 + (b^-^2a^2 + 3a^2b^-^2)^-^1 \\ \\ \\ \dfrac{1}{a^2}+ ( \dfrac{1}{b^2}.a^2 + 3a^2. \dfrac{1}{b^2})^-^1 \\ \\ \\ \dfrac{1}{a^2}+ ( \dfrac{a^2}{b^2}+ \dfrac{3a^2}{b^2})^-^1 \\ \\ \\ \dfrac{1}{a^2}+ ( \dfrac{4a^2}{b^2})^-^1 \\ \\ \\ \dfrac{1}{a^2}+ \dfrac{b^2}{4a^2} \\ \\ \\ =\ \textgreater \ \dfrac{4 + b^2}{4a^2}$