(\dfrac{1}{a-b} -\dfrac{b}{a^2-b^2} )÷\dfrac{a}{a+b}

= \Big[ \dfrac{1}{a-b} -\dfrac{b}{(a-b)(a+b)} \Big] \dfrac{a+b}{a}

=\dfrac{a+b}{a(a-b)}- \dfrac{b}{a(a-b)}

=\dfrac{1}{a-b}