Giải thích các bước giải:

Ta có:

$A=\dfrac1{1-x}+\dfrac1{1+x}+\dfrac2{1+x^2}+\dfrac4{1+x^4}+\dfrac8{1+x^8}$

$\to A=(\dfrac1{1-x}+\dfrac1{1+x})+\dfrac2{1+x^2}+\dfrac4{1+x^4}+\dfrac8{1+x^8}$

$\to A=\dfrac2{(1-x)(1+x)}+\dfrac2{1+x^2}+\dfrac4{1+x^4}+\dfrac8{1+x^8}$

$\to A=\dfrac2{1-x^2}+\dfrac2{1+x^2}+\dfrac4{1+x^4}+\dfrac8{1+x^8}$

$\to A=\dfrac4{(1-x^2)(1+x^2)}+\dfrac4{1+x^4}+\dfrac8{1+x^8}$

$\to A=\dfrac4{1-x^4}+\dfrac4{1+x^4}+\dfrac8{1+x^8}$

$\to A=\dfrac8{(1-x^4)(1+x^4)}+\dfrac8{1+x^8}$

$\to A=\dfrac8{1-x^8}+\dfrac8{1+x^8}$

$\to A=\dfrac{16}{(1-x^8)(1+x^8)}$

$\to A=\dfrac{16}{1-x^{16}}$