Answer
$\text{LCD: }
84x^2y
\\\\\text{Equivalent of 1st Expression: }
\dfrac{49}{84x^2y}
\\\\\text{Equivalent of 2nd Expression: }
\dfrac{9x}{84x^2y}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the $LCD$ of the given expressions, $
\dfrac{7}{12x^2y}
$ and $
\dfrac{3}{28xy}
,$ express the denominators in factored form. Then take the highest exponent of each factor. Finally use the $LCD$ to find the required equivalent expression for the given.
$\bf{\text{Solution Details:}}$
In factored form, the given expressions are equivalent to
\begin{array}{l}\require{cancel}
\dfrac{7}{2^2(3)(x^2)(y)}
\text{ and }
\dfrac{3}{2^2(7)(x)(y)}
.\end{array}
Taking the highest exponent of each factor, then the $LCD$ is
\begin{array}{l}\require{cancel}
2^2(3)(7)(x^2)(y)
\\\\=
84x^2y
.\end{array}
Multiplying the given expression by an expression equal to $1$ such that the denominator becomes the $LCD,$ then the given expressions are equivalent to
\begin{array}{l}\require{cancel}
\dfrac{7}{12x^2y}\cdot\dfrac{7}{7}=
\dfrac{49}{84x^2y}
\\\\\text{ and }\\\\
\dfrac{3}{28xy}\cdot\dfrac{3x}{3x}=
\dfrac{9x}{84x^2y}
.\end{array}
Hence, the needed pieces of information are as follows:
\begin{array}{l}\require{cancel}
\text{LCD: }
84x^2y
\\\\\text{Equivalent of 1st Expression: }
\dfrac{49}{84x^2y}
\\\\\text{Equivalent of 2nd Expression: }
\dfrac{9x}{84x^2y}
.\end{array}
