Question

1) ((m-(2*sqrt(mn))+n)/(m-n))
2) ((a+3*sqrt(a))/(a-9)
3) a/(a-1)-(sqrt(a))/(sqrt(a)+1)

Answer 1

1)
$\frac{m - 2 \sqrt{mn} + n }{m - n} = \frac{ {( \sqrt{m} - \sqrt{n} )}^{2} }{( \sqrt{m} - \sqrt{n} )( \sqrt{m} + \sqrt{n}) } = \frac{ \sqrt{m} - \sqrt{n} }{ \sqrt{m} + \sqrt{n} }$
2)
$\frac{a + 3 \sqrt{a} }{a - 9} = \frac{ \sqrt{a}( \sqrt{a} + 3)}{( \sqrt{a} - 3)( \sqrt{a} + 3)} = \frac{ \sqrt{a} }{ \sqrt{a} - 3}$
3)
$\frac{a}{a - 1} - \frac{ \sqrt{a} }{ \sqrt{a} + 1 } = \frac{a}{( \sqrt{a} - 1)( \sqrt{a} + 1) } - \frac{ \sqrt{a}( \sqrt{a} - 1) }{( \sqrt{a} + 1)( \sqrt{a} - 1) } = \frac{a - a + \sqrt{a} }{a - 1} = \frac{ \sqrt{a} }{a - 1}$