Question

Determine a diferença 8+x sobre 8-x - 8-x sobre 8+ x e calcule seu valor numérico para x= 2

Answer 1

Bom dia

$a ) \dfrac{8+x}{8-x}- \dfrac{8-x}{8+x}=\dfrac{(8+x)(8+x)-(8-x)(8-x)}{(8-x)(8+x)}= \\ \\ \\ \dfrac{(64+16x+x^{2})-(64-16x+x^{2})}{64-x^{2}} =\\ \\ \\ \dfrac{64+16x+x^{2}-64+16x-x^{2})}{64-x^{2}} = \boxed{ \dfrac{32x}{64-x^{2}} }$

$b) \dfrac{32*2}{64-2^{2}} =\dfrac{64}{60}= \boxed{ \dfrac{16}{15} }$