$$\frac{a^{2}b^{2}+3ab}{4a^{2}-1}\times\frac{2a+1}{ab+3}$$
$\frac{ab}{2a-1}$
$$\frac{\left(a^{2}b^{2}+3ab\right)\left(2a+1\right)}{\left(4a^{2}-1\right)\left(ab+3\right)}$$
$$\frac{ab\left(2a+1\right)\left(ab+3\right)}{\left(2a-1\right)\left(2a+1\right)\left(ab+3\right)}$$
$$\frac{ab}{2a-1}$$
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