If \({\sin ^{ - 1}}\frac{{2p}}{{1 + p2}} - {\cos ^{ - 1}}\frac{{1 - {q^2}}}{{1 + {q^2}}} = {\tan ^{ - 1}}\frac{{2x}}{{1 - {x^2}}}\), then what is x equal to?

• A. \(\frac{{p + q}}{{1 + pq}}\)
• B. \(\frac{{p - q}}{{1 + pq}}\)
• C. \(\frac{{pq}}{{1 + pq}}\)
• D. \(\frac{{p + q}}{{1 - pq}}\)