If \(\frac{{4a\; + \;7b}}{{4c\; +\; 7d}} = \frac{{4a\; - \;7b}}{{4c\; -\; 7d}}\), then which one of the following is correct?

• A. \(\frac{a}{b} = \frac{c}{d}\)
• B. \(\frac{a}{b} = \frac{c}{b}\)
• C. \(\frac{a}{b} = \frac{d}{c}\)
• D. \(\frac{{4a}}{{7b}} = \frac{c}{d}\)