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Dễ thôi :)
\(\frac{45}{19}-\left\{\frac{1}{2}+\left[\frac{1}{3}+\left(\frac{1}{4}\right)^{-1}\right]^{-1}\right\}^{-1}\)
\(=\frac{45}{19}-\left\{\frac{1}{2}+\left[\frac{1}{3}+4\right]^{-1}\right\}^{-1}\)
'\(=\frac{45}{19}-\left\{\frac{1}{2}+\frac{3}{13}\right\}^{-1}\)
\(=\frac{45}{19}-\frac{26}{19}\)
\(=\frac{19}{19}=1\)
=45/19-(1/2+(1/3+4)^-1)^-1
=45/19-(1/2+(13/3)^-1)^-1
=45/19-(1/2+3/13)^-1
=45/19-(19/26)^-1
=45/19-26/19=19/19=1
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{\left(1+17\right).\left(1+\frac{17}{2}\right).\left(1+\frac{17}{3}\right)...\left(1+\frac{17}{19}\right)}{\left(1+19\right).\left(1+\frac{19}{2}\right).\left(1+\frac{19}{3}\right)...\left(1+\frac{19}{17}\right)}\)
\(=\frac{18.\frac{19}{2}.\frac{20}{3}...\frac{36}{19}}{20.\frac{21}{2}.\frac{22}{3}...\frac{36}{17}}=\frac{18.19.20...36}{1.2.3...19}:\frac{20.21.22...36}{1.2.3...17}\)
\(=\frac{18.19.20...36}{1.2.3...19}.\frac{1.2.3...17}{20.21.22....36}=\frac{1.2.3...17.18...36}{1.2.3...19.20...36}=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
cho công thức tổng quát nè (do tui tự nghĩ ra đó :))
\(\left(a+b\right)\left(\frac{1}{?}\right)=\frac{a+b}{?}\) dựa vô đây nhân (1+17) và (1+19) và từng cái ngoặc kia là đc
\(A=\frac{\frac{1+17}{1}\cdot\frac{2+17}{2}\cdot\frac{3+17}{3}\cdot...\cdot\frac{19+17}{19}}{\frac{1+19}{1}\cdot\frac{2+19}{2}\cdot\frac{3+19}{3}\cdot...\cdot\frac{17+19}{17}}=\frac{18\cdot19\cdot20\cdot...\cdot36}{1\cdot2\cdot3\cdot...\cdot19}:\frac{20\cdot21\cdot22\cdot...\cdot36}{1\cdot2\cdot3\cdot...\cdot17}\)
\(=\frac{18\cdot19}{18\cdot19}=1\)