Answer
$\dfrac{19}{9x^2-30x+25}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\dfrac{(2x+3)\cdot3-(3x-5)\cdot2}{(3x-5)^2}
,$ use the Distributive Property first. Then remove the grouping symbols and combine like terms. Finally, use special products to simplify the denominator.
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{(2x\cdot3+3\cdot3)-(3x\cdot2-5\cdot2)}{(3x-5)^2}
\\\\=
\dfrac{(6x+9)-(6x-10)}{(3x-5)^2}
.\end{array}
Removing the grouping symbols and then combining like terms, the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{6x+9-6x+10}{(3x-5)^2}
\\\\=
\dfrac{19}{(3x-5)^2}
.\end{array}
Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{19}{(3x)^2-2(3x)(5)+(5)^2}
\\\\=
\dfrac{19}{9x^2-30x+25}
.\end{array}
