Question

√x2+25 -- √x2+9 =8/x

Answer 1

$\sqrt{x^2+25} - \sqrt{x^2+9} \\ \\ = \sqrt{25(1+ \frac{x^2}{25}) } - \sqrt{9(1+ \frac{x^2}{9})} \\ \\ =5(1+ \frac{x^2}{25})^{ \frac{1}{2} }-3(1+ \frac{x^2}{9})^{ \frac{1}{2} }\\ \\ =5(1+ \frac{x^2}{50})-3(1+ \frac{x^2}{18})\\ \\ =5+ \frac{x^2}{10}-3- \frac{x^2}{6}\\ \\ =2- \frac{x^2}{15}$