Answer
\[\left( \frac{193}{432} \right)\].
Work Step by Step
This expression can be reduced by the determination of LCM of denominators of both rational numbers.
As,\[108={{2}^{2}}\times {{3}^{3}}\] and\[144={{2}^{4}}\times {{3}^{2}}\]. LCM of \[108\] and 144 is\[{{2}^{4}}\times {{3}^{3}}=432\].
Now, divide\[432\]by\[108\] and \[144\] both.
So,
\[\begin{align}
& \left( \frac{432}{108} \right)=4 \\
& \left( \frac{432}{144} \right)=3
\end{align}\]
As,
\[\left( \frac{a}{b} \right)=\left( \frac{a.c}{b.c} \right)\]
So,
\[\begin{align}
& \left( \frac{7}{108} \right)=\left( \frac{7\times 4}{108\times 4} \right) \\
& =\left( \frac{28}{432} \right)
\end{align}\]
And,
\[\begin{align}
& \left( \frac{55}{144} \right)=\left( \frac{55\times 3}{144\times 3} \right) \\
& =\left( \frac{165}{432} \right)
\end{align}\]
Now,
\[\begin{align}
& \left( \frac{7}{108}+\frac{55}{144} \right)=\left( \frac{28}{432}+\frac{165}{432} \right) \\
& =\left( \frac{193}{432} \right)
\end{align}\]
Therefore, the reduced value of the expression\[\left( \frac{7}{108}+\frac{55}{144} \right)\]is \[\left( \frac{193}{432} \right)\].
