¡Claro! Vamos a resolver cada una de las operaciones con fracciones de forma detallada paso a paso.
### a. [tex]\(\frac{1}{6} + \frac{4}{5}\)[/tex]
Para sumar fracciones, primero encontramos un denominador común:
[tex]\[
\frac{1}{6} + \frac{4}{5} = \frac{5 \times 1}{30} + \frac{6 \times 4}{30} = \frac{5}{30} + \frac{24}{30} = \frac{5 + 24}{30} = \frac{29}{30}
\][/tex]
[tex]\[
\boxed{\frac{29}{30}}
\][/tex]
### b. [tex]\(\frac{7}{10} - \frac{1}{8}\)[/tex]
Primero encontramos un denominador común:
[tex]\[
\frac{7}{10} - \frac{1}{8} = \frac{7 \times 8}{80} - \frac{1 \times 10}{80} = \frac{56}{80} - \frac{10}{80} = \frac{56 - 10}{80} = \frac{46}{80} = \frac{23}{40}
\][/tex]
[tex]\[
\boxed{\frac{23}{40}}
\][/tex]
### c. [tex]\(\frac{6}{14} + \frac{8}{-21}\)[/tex]
Primero simplificamos las fracciones:
[tex]\[
\frac{6}{14} = \frac{3}{7}, \quad \frac{8}{-21} = -\frac{8}{21}
\][/tex]
Luego encontramos un denominador común:
[tex]\[
\frac{3}{7} + \left(-\frac{8}{21}\right) = \frac{3 \times 3}{21} - \frac{8}{21} = \frac{9}{21} - \frac{8}{21} = \frac{9 - 8}{21} = \frac{1}{21}
\][/tex]
[tex]\[
\boxed{\frac{1}{21}}
\][/tex]
### d. [tex]\(-\frac{5}{4} + \frac{7}{3}\)[/tex]
Encontramos un denominador común:
[tex]\[
-\frac{5}{4} + \frac{7}{3} = \frac{-15}{12} + \frac{28}{12} = \frac{-15 + 28}{12} = \frac{13}{12}
\][/tex]
[tex]\[
\boxed{\frac{13}{12}}
\][/tex]
### e. [tex]\(\frac{6}{5} + \frac{-3}{8} - \frac{8}{-5}\)[/tex]
La tercera fracción se vuelve positiva:
[tex]\[
\frac{8}{-5} = -\frac{8}{5}
\][/tex]
Entonces, sumamos:
[tex]\[
\frac{6}{5} - \frac{3}{8} + \frac{8}{5} = \frac{6 \times 8 + 8 \times (-3) + 8 \times 8}{40} = \frac{48 - 3 \times 5 + 64}{5} = \frac{48 - 15 + 64}{40} = \frac{163}{40} = \boxed{\frac{97}{40}}
\][/tex]
### f. [tex]\(\frac{6}{7} - \frac{-3}{14} - \frac{18}{5}\)[/tex]
Simplificamos pasos:
[tex]\[
\frac{6}{7} + \frac{3}{14} = \frac{12}{14} + \frac{3}{14} = \frac{15}{14} - \frac{18}{5}
\][/tex]
Adquiriendo denominador común:
[tex]\[
\frac{-177}{70}
\][/tex]
### g. [tex]\(-\frac{12}{35} - \frac{6}{14}\)[/tex]
Primero simplificamos:
[tex]\[
-\frac{12}{35} - \frac{3}{7}
\][/tex]
[tex]\[
\boxed{\frac{-27}{35}}
\][/tex]
### h. [tex]\(\frac{1}{2} - \frac{1}{3} + \frac{2}{5}\)[/tex]
[tex]\[
\frac{15}{30} + \frac{-10}{30} + \frac{12}{30} = \frac}{30} = \boxed{\frac{17}{30}}
\][/tex]
