Question

√a+x-√a-x by √a+x+√a-x

Answer 1

Answer:

$\frac{ \sqrt{a + x} - \sqrt{a - x} }{ \sqrt{a + x} + \sqrt{a - x} }$

$rationalise \: the \: dinominator$

$= \frac{ \sqrt{a + x} - \sqrt{a - x} }{ \sqrt{a + x} + \sqrt{a - x} } \times \frac{ \sqrt{a + x} - \sqrt{a + x} }{ \sqrt{a + x} - \sqrt{a - x} }$

$= \frac{ {( \sqrt{a + x} - \sqrt{a -x} )}^{2} }{ {( \sqrt{a + x} )}^{2} - ({ \sqrt{a - x} }^{2} ) }$

$= \frac{ {( \sqrt{a + x})}^{2} - 2. \sqrt{a + x} . \sqrt{a - x} + {( \sqrt{a - x} }^{2}) }{a + x - (a - x)}$

$= \frac{( { \sqrt{a + x} })^{2} - 2. \sqrt{a + x} . \sqrt{a - x} + { \sqrt{(a - x} )}^{2} }{2x}$