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**Prove It** First of all, this is VERY hard to read, some brackets would help. I assume that your expression is $\displaystyle \displaystyle \begin{align*} \frac{5a}{6bc^2} + \frac{3b}{8a^2c} \end{align*}$, if you look at the factors in each denominator, you have $\displaystyle \displaystyle \begin{align*} 2 \cdot 3 \cdot b \cdot c \cdot c \end{align*}$, and in the second you have $\displaystyle \displaystyle \begin{align*} 2 \cdot 2 \cdot 2 \cdot a \cdot a \cdot c \end{align*}$. That means when you are trying to get the lowest common denominator, in your first denominator, you are missing just $\displaystyle \displaystyle \begin{align*} 2\cdot 2 \cdot a \cdot a \end{align*}$, while in the second you are missing $\displaystyle \displaystyle \begin{align*} 3 \cdot b \cdot c \end{align*}$.

So when you write these with the lowest common denominator

$\displaystyle \displaystyle \begin{align*} \frac{5a}{6bc^2} + \frac{3b}{8a^2c} &= \frac{5a \cdot 2 \cdot 2 \cdot a \cdot a}{6bc^2 \cdot 2 \cdot 2 \cdot a \cdot a} + \frac{3b \cdot 3 \cdot b \cdot c}{8a^2c \cdot 3 \cdot b \cdot c} \\ &= \frac{20a^3}{24a^2 b c^2} + \frac{9b^2 c}{24 a^2 b c^2} \end{align*}$