Answer
$\dfrac{9}{20}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the $LCD$ to convert the terms of the given expression, $
\dfrac{3}{4}-\dfrac{3}{10}
,$ to similar terms. Once expressed as similar terms, operate on the numerators and copy the common denominator.
$\bf{\text{Solution Details:}}$
The prime factorization of $
4
$ is $
4=2^2.$ The prime factorization of $
10
$ is $
10=2^1\cdot5^1.$ Getting each factor with the highest exponent, then the $
LCD=2^2\cdot5^1=20
.$ Converting the terms of the given expression to similar terms by using the $LCD$ results to
\begin{array}{l}\require{cancel}
\dfrac{3}{4}\cdot\dfrac{5}{5}-\dfrac{3}{10}\cdot\dfrac{2}{2}
\\\\=
\dfrac{15}{20}-\dfrac{6}{20}
\\\\=
\dfrac{15-6}{20}
\\\\=
\dfrac{9}{20}
.\end{array}
