Question

Dados A= a+1/b+1 e B= a-1/b+1, determine A²-B²​

Answer 1

Resposta:

$A^{2}-B^{2}=\frac{4a}{b^{2}+2b+1}$

Explicação passo-a-passo:

$A^{2}-B^{2}=[\frac{(a+1)^{2}}{(b+1)^2}]- [\frac{(a-1)^{2}}{(b+1)^2}]$

$A^{2}-B^{2}=\frac{(a+1)^{2} - (a-1)^{2}}{(b+1)^2}$

$A^{2}-B^{2}=\frac{(a+1).(a+1)-(a-1).(a-1)}{(b+1).(b+1)}$

$A^{2}-B^{2}=\frac{(a.a + a.1 + 1.a +1.1)-(a.a - a.1 - 1.a +1.1)}{b.b+b.1+1.b+1.1}$

$A^{2}-B^{2}=\frac{(a^{2} + 2a +1)-(a^{2} -2a +1)}{(b^{2}+2b+1)}$

$A^{2}-B^{2}=\frac{a^{2} + 2a +1-a^{2} +2a -1}{(b^{2}+2b+1)}$

$A^{2}-B^{2}=\frac{4a}{b^{2}+2b+1}$