Question

BT5 : Rút gọn

(1/a-b) + (1/a+b ) + (2/a²+b² ) + ( 4.a³/a⁴+b⁴ ) + ( 8.a⁷/a⁸+b⁸ )

Answer 1

\(=\dfrac{a+b+a-b}{a^2-b^2}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3}{a^4+b^4}+\dfrac{8a^7}{a^8+b^8}\)

\(=\dfrac{2a^3+2a^2b^2+2a^3-2ab^2}{a^4-b^4}+\dfrac{4a^3}{a^4+b^4}+\dfrac{8a^7}{a^8+b^8}\)

\(=\dfrac{4a^7+4a^3b^4+4a^7-4a^3b^4}{a^8-b^8}+\dfrac{8a^7}{a^8+b^8}\)

\(=\dfrac{8a^7}{a^8-b^8}+\dfrac{8a^7}{a^8+b^8}\)

\(=\dfrac{8a^{15}+8a^7b^8+8a^{15}-8a^7b^8}{a^{16}-b^{16}}=\dfrac{16a^{15}}{a^{16}-b^{16}}\)