Answer
$\dfrac{2a}{2a-3}$
Work Step by Step
The given expression, $
\dfrac{a+b}{2a-3}-\dfrac{a-b}{3-2a}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{a+b}{2a-3}-\dfrac{a-b}{-(-3+2a)}
\\\\=
\dfrac{a+b}{2a-3}-\dfrac{a-b}{-(2a-3)}
\\\\=
\dfrac{a+b}{2a-3}+\dfrac{a-b}{2a-3}
.\end{array}
Since the fractions are similar, then copy the common denominator and add/subtract the numerators. Hence, the expression, $
\dfrac{a+b}{2a-3}+\dfrac{a-b}{2a-3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{a+b+a-b}{2a-3}
\\\\=
\dfrac{2a}{2a-3}
.\end{array}
