<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Simplify \(\frac{x^2 - 3x - 10}{x - 5} \div \frac{x^2 - 4}{3 + x}\).<span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">\(n\) is a positive integer.<br>Show that, for all \(n\), \((2n + 3)^2 - (2n + 1)^2\) is a multiple of \(8\).<span class="inline-marks">[2]</span></div></li></ol>

Simplify \(\frac{x^2 - 3x - 10}{x - 5} \div \frac{x^2 - 4}{3 + x}\).

\(n\) is a positive integer.
Show that, for all \(n\), \((2n + 3)^2 - (2n + 1)^2\) is a multiple of \(8\).

Algebraic Identities

Algebraic Identities