a.\(A=\dfrac{3a+5\sqrt{a}-4}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+3\right)}-\dfrac{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)-\left(\sqrt{a}+3\right)\left(\sqrt{a}+3\right)}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-1\right)}\)
\(A=\dfrac{3a+5\sqrt{a}-4}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+3\right)}-\dfrac{\left(a-1\right)-\left(\sqrt{a}+3\right)^2}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-1\right)}\)
\(A=\dfrac{3a+5\sqrt{a}-4}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+3\right)}-\dfrac{\left(a-1\right)-\left(a+6\sqrt{a}+9\right)}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-1\right)}\)
\(A=\dfrac{3a+5\sqrt{a}-4}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+3\right)}-\dfrac{-6\sqrt{a}-10}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-1\right)}\)
\(A=\dfrac{3a-\sqrt{a}-14}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+3\right)}\)
\(A=\dfrac{\left(3\sqrt{a}-7\right)\left(\sqrt{a}+2\right)}{\left(\sqrt{a-1}\left(\sqrt{a}+3\right)\right)}\)
b.\(A=-\dfrac{1}{2}\)
\(\Leftrightarrow-\dfrac{1}{2}=\dfrac{\left(3\sqrt{a}-7\right)\left(\sqrt{a}+2\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+3\right)}\)
\(\Leftrightarrow-\left(a+2\sqrt{a}-3\right)=2\left(3a-\sqrt{a}-14\right)\)
\(\Leftrightarrow-a-2\sqrt{a}+6=6a-2\sqrt{a}-28\)
\(\Leftrightarrow7a-34=0\)
\(\Leftrightarrow7a=34\)
\(\Leftrightarrow a=\dfrac{34}{7}\)
