Simplify: $\left(\frac{7}{9} + \frac{5}{6}\right) \div \left(\frac{11}{12} - \frac{2}{5}\right)$

Question

Accepted Answer

Simplify: $\left(\frac{7}{9} + \frac{5}{6}ight) \div \left(\frac{11}{12} - \frac{2}{5}ight)$
(a) $\frac{262}{97}$ (b) $\frac{272}{53}$ (c) $\frac{282}{87}$ (d) $\frac{290}{93}$
Solution:
First, simplify the first bracket:
$$ \frac{7}{9} + \frac{5}{6} $$
LCM of 9 and 6 is 18.
$$ = \frac{14}{18} + \frac{15}{18} $$
$$ = \frac{29}{18} $$
Now, simplify the second bracket:
$$ \frac{11}{12} - \frac{2}{5} $$
LCM of 12 and 5 is 60.
$$ = \frac{55}{60} - \frac{24}{60} $$
$$ = \frac{31}{60} $$
Now, divide both values:
$$ \frac{29}{18} \div \frac{31}{60} $$
$$ = \frac{29}{18} 	imes \frac{60}{31} $$
$$ = \frac{29 	imes 10}{3 	imes 31} $$
$$ = \frac{290}{93} $$
Therefore, the simplified value is:
$$ \boxed{\frac{290}{93}} $$
Final Answer: **Option (d) $\frac{290}{93}$**

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