Question

Rút gọn các phân thức sau:

A = \(\dfrac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\) ; B= \(\dfrac{8020}{2004.2006-2003.2005}\)

Answer 1

A = \(\dfrac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}=\dfrac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3.3^{19}-7.2^{29}.3^{18}}=\dfrac{2^{29}.3^{18}\left(5.2-3^2\right)}{2^{18}.3^{18}\left(5.3-7.2\right)}=2\)

B = \(\dfrac{8020}{2004.2006-2003.2005}\)

Đặt x = 2004, ta có:

\(\dfrac{4x+2}{x\left(x+2\right)-\left(x-1\right)\left(x+1\right)}=\dfrac{4x+2}{2x+1}=\dfrac{2\left(2x+1\right)}{2x+1}=2\)