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[vietdungdc]

Rút gọn phân thức

a)A=$\frac{\left ( a^{2}+b^{2}+c^{2} \right )\left ( a+b+c \right )^{2}+\left ( ab+bc+ca \right )^{2}}{\left ( a+b+c \right )^{2}-\left ( ab+bc+ca \right )}$

b)B=$\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^{2}}+\frac{4}{1+x^{4}}+\frac{8}{1+x^{8}}+\frac{16}{1+x^{16}}$

Edited by vietdungdc, 02-12-2015 - 20:34.

[NTA1907]

Rút gọn phân thức

b)B=$\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^{2}}+\frac{4}{1+x^{4}}+\frac{8}{1+x^{8}}+\frac{16}{1+x^{16}}$

$B=\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^{2}}+\frac{4}{1+x^{4}}+\frac{8}{1+x^{8}}+\frac{16}{1+x^{16}}$

    =$\frac{2}{1-x^{2}}+\frac{2}{1+x^{2}}+\frac{4}{1+x^{4}}+\frac{8}{1+x^{8}}+\frac{16}{1+x^{16}}$

    =$\frac{4}{1-x^{4}}+\frac{4}{1+x^{4}}+\frac{8}{1+x^{8}}+\frac{16}{1+x^{16}}$

    =$\frac{8}{1-x^{8}}+\frac{8}{1+x^{8}}+\frac{16}{1+x^{16}}$

    =$\frac{16}{1-x^{16}}+\frac{16}{1+x^{16}}=\frac{32}{1-x^{32}}$