Question

Questão 19 de frações algébricas do livro tópicos de álgebra elementar. ​

Answer 1

Resposta:

desculpa eu responderia mais ñ sei fazer isso ainda eu to no 7 ano

Answer 2

Resposta:

Explicação passo-a-passo:

$ab^{3}=\sqrt{2}+1 (I)\\\\a^{3}b=\sqrt{2}-1(II)\\\\Fazendo\\(I).(II)\\\\ab^{3}.a^{3}b=(\sqrt{2}+1)(\sqrt{2}-1)\\\\a^{4}.b^{4}=2-1\\  \\a^{4}.b^{4}=1$

$mmc(a^{4}+1,b^{4}+1)=(a^{4}+1)(b^{4}+1)\\\\\dfrac{a^{4}(b^{4}+1)^{2} +b^{4}(a^{4}+1)^{2}}{(a^{4}+1)(b^{4}+1)}=\\\\\\\\=\dfrac{a^{4}(b^{8}+2b^{4} +1)+b^{4}(a^{8}+2a^{4}+1)}{a^{4}b^{4} +a^{4}+b^{4}+1}=\\\\\\=\dfrac{a^{4}b^{8}+2a^{4}b^{4} +a^{4}+a^{8}b^{4}+2a^{4}b^{4}+b^{4}}{1 +a^{4}+b^{4}+1}=\\\\\\=\dfrac{(a^{4}b^{4})b^{4}+2a^{4}b^{4} +a^{4}+a^{4}(a^{4}b^{4})+2a^{4}b^{4}+b^{4}}{a^{4}+b^{4}+2}=$

$=\dfrac{b^{4}+2+a^{4}+a^{4}+2+b^{4}}{a^{4}+b^{4}+2}=\\\\\\=\dfrac{2a^{4}+2b^{4}+4}{a^{4}+b^{4}+2}=\\\\\\=\dfrac{2(a^{4}+b^{4}+2)}{(a^{4}+b^{4}+2)}=\\\\\\=2$