$$\frac { 4 p ^ { 2 } - 1 } { p ^ { 2 } - 1 } \times \frac { p q + q } { 4 p - 2 }$$
$\frac{q\left(2p+1\right)}{2\left(p-1\right)}$
$$\frac{\left(4p^{2}-1\right)\left(pq+q\right)}{\left(p^{2}-1\right)\left(4p-2\right)}$$
$$\frac{q\left(2p-1\right)\left(p+1\right)\left(2p+1\right)}{2\left(p-1\right)\left(2p-1\right)\left(p+1\right)}$$
$$\frac{q\left(2p+1\right)}{2\left(p-1\right)}$$
$$\frac{2pq+q}{2p-2}$$
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$\frac{2pq+q}{2\left(p-1\right)}$
