Rút gọn các biểu thức sau (x + 1) / (x + 2) . ((x + 2) / (x + 3) : (x + 3) / (x + 1))
Rút gọn các biểu thức sau:
\(\frac{{x + 1}}{{x + 2}}.\left( {\frac{{x + 2}}{{x + 3}}:\frac{{x + 3}}{{x + 1}}} \right)\).
\(\frac{{x + 1}}{{x + 2}}.\left( {\frac{{x + 2}}{{x + 3}}:\frac{{x + 3}}{{x + 1}}} \right)\)
\( = \frac{{x + 1}}{{x + 2}}.\left( {\frac{{x + 2}}{{x + 3}}.\frac{{x + 1}}{{x + 3}}} \right)\)
\( = \frac{{x + 1}}{{x + 2}}.\frac{{\left( {x + 2} \right).\left( {x + 1} \right)}}{{{{\left( {x + 3} \right)}^2}}}\)
\( = \frac{{\left( {x + 1} \right)\left( {x + 2} \right).\left( {x + 1} \right)}}{{\left( {x + 2} \right){{\left( {x + 3} \right)}^2}}}\)
\( = \frac{{{{\left( {x + 1} \right)}^2}}}{{{{\left( {x + 3} \right)}^2}}} = {\left( {\frac{{x + 1}}{{x + 3}}} \right)^2}\).