Operaciones combinadas con fracciones

Os traigo unos ejercicios que combinan todo lo visto anteriormente en las fracciones.

\(\bullet3\cdot \left( \dfrac {2} {3}-\dfrac {7} {5}\right) -5\cdot \left( \dfrac {14} {21}+\dfrac {3} {9}\right)=3\cdot \left( \dfrac {2} {3}-\dfrac {7} {5}\right) -5\left( \dfrac {2} {3}+\dfrac {1} {3}\right)= \)

\(\enclose{updiagonalstrike}{3}\cdot \left( \dfrac {2\cdot 5-7\cdot 3} {\enclose{updiagonalstrike}{3}\cdot 5}\right) -5\cdot \dfrac {\enclose{updiagonalstrike}{3}} {\enclose{updiagonalstrike}{3}}=-\dfrac {11} {5}-5=\dfrac {-11-5\cdot 5} {5}=\boxed{\dfrac {-36} {5}}\)

\(\bullet\left( \dfrac {5} {2}-\dfrac {2} {3}\right) ^{2}+\dfrac {5} {12}-\dfrac {1} {9}=\left( \dfrac {5\cdot 3-2\cdot 2} {6}\right) +\dfrac {5} {12}-\dfrac {1} {9}\)

\(\left( \dfrac {11} {6}\right) ^{2}+\dfrac {5} {12}-\dfrac {1} {9}=\dfrac {121} {36}+\dfrac {5} {12}-\dfrac {1} {9}=\dfrac {121\cdot 1+5\cdot 3-1\cdot 4} {36}=\)

\(=\dfrac {132} {36}=\boxed{\dfrac {11} {3}}\)

\(\bullet\left( \dfrac {3} {5}-\dfrac {1} {2}\right) :\dfrac {3} {10}+\left( \dfrac {3} {2}+2\right) \cdot \left( 2-\dfrac {12} {7}\right) =\)

\(\left( \dfrac {3\cdot 2-1\cdot 5} {10}\right) =\dfrac {3} {10}+\left( \dfrac {3\cdot 1+2\cdot 2} {2}\right) \cdot \left( \dfrac {27-12\cdot 1} {7}\right)=\)

\(=\dfrac {1} {\enclose{updiagonalstrike}{10}}\cdot \dfrac {\enclose{updiagonalstrike}{10}} {3}+\dfrac {\enclose{updiagonalstrike}{7}} {\enclose{updiagonalstrike}{2}}\cdot \dfrac {\enclose{updiagonalstrike}{2}} {\enclose{updiagonalstrike}{7}}=\dfrac {1} {3}+1=\boxed{\dfrac {4} {3}}\)

\(\bullet\dfrac {\left( \dfrac {5} {6}+\dfrac {2} {3}\right) -\left( \dfrac {3} {2}-\dfrac {1} {4}\right) } {\left( \dfrac {3} {2}-\dfrac {4} {5}\right) -\left( \dfrac {1} {5}-\dfrac {2} {3}\right) -\dfrac {1} {2}}=\)

\(=\dfrac {\left( \dfrac {5\cdot 1+2\cdot 2} {6}\right) -\left( \dfrac {3\cdot 2-1\cdot 1} {4}\right) } {\left( \dfrac {3\cdot 5-4\cdot 2} {10}\right) -\left( \dfrac {1-3-2\cdot 5} {15}\right) -\dfrac {1} {2}}=\dfrac {\dfrac {10} {6}-\dfrac {5} {4}} {\dfrac {7} {10}-\dfrac {7} {15}-\dfrac {1} {2}}\)

\(\dfrac {\dfrac {102-15\cdot 3} {12}} {\dfrac {7\cdot 3-7\cdot 2-1\cdot 15} {30}}=\dfrac {-\dfrac {25} {12}} {-\dfrac {22} {30}}=\dfrac {25} {12}\cdot \dfrac {30} {22}=\dfrac {5^{2}\cdot\enclose{updiagonalstrike} {2}\cdot \enclose{updiagonalstrike}{3}\cdot 5} {\enclose{updiagonalstrike}{3}\cdot 2^{2}\cdot \enclose{updiagonalstrike}{2}\cdot 11}=\boxed{\dfrac {125} {44}}\)