Question

arrange the expressions in the correct sequence to rationalize the denominator of the expression -(2)/(\sqrt(x+y-2)-\sqrt(x+y+2))

Answer 1

Answer:

$\frac{\sqrt{x+y-2}+\sqrt{x+y+2}}{2}$

Step-by-step explanation:

Given expression :

$\frac{-2}{\sqrt{x+y-2}-\sqrt{x+y+2}}$

Now, we solve this expression by rationalizing method

$\frac{-2}{\sqrt{x+y-2}-\sqrt{x+y+2}}\times\frac{\sqrt{x+y-2}+\sqrt{x+y+2}}{\sqrt{x+y-2}+\sqrt{x+y+2}}$  

$\frac{-2(\sqrt{x+y-2}+\sqrt{x+y+2})}{x+y-2-x-y-2}$  

(using  $(a+b)(a-b)=a^2-b^2$)

$\frac{-2(\sqrt{x+y-2}+\sqrt{x+y+2})}{-4}$

$\frac{\sqrt{x+y-2}+\sqrt{x+y+2}}{2}$

this is the required arrangement which result the expression by rationalizing

Answer 2

We have to rationalize the denominator:
$\frac{-2}{ \sqrt{x+y-2} - \sqrt{x+y+2} } = \\ \frac{-2}{ \sqrt{x+y-2} - \sqrt{x+y+2} }* \frac{ \sqrt{x+y-2}+ \sqrt{x+y+2} }{ \sqrt{x+y-2}+ \sqrt{x+y+2} }= \\ \frac{-2*( \sqrt{x+y-2}+ \sqrt{x+y+2}) }{x+y-2-(x+y+2)}= \\ \frac{-2*( \sqrt{x+y-2}+ \sqrt{x+y+2}) }{x+y-2-x-y-2}= \\ \frac{-2*( \sqrt{x+y-2}+ \sqrt{x+y+2} }{-4}= \\ \frac{ \sqrt{x+y-2}+ \sqrt{x+y+2} }{2}$