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

We have to rationalize the denominator:
[tex] \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} [/tex]

Answer Link

DodieZollner DodieZollner · Answer 2 · 2019-01-02T07:23:47+01:00

Answer:

[tex]\frac{\sqrt{x+y-2}+\sqrt{x+y+2}}{2}[/tex]

Step-by-step explanation:

Given expression :

[tex]\frac{-2}{\sqrt{x+y-2}-\sqrt{x+y+2}}[/tex]

Now, we solve this expression by rationalizing method

[tex]\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}}[/tex]

[tex]\frac{-2(\sqrt{x+y-2}+\sqrt{x+y+2})}{x+y-2-x-y-2}[/tex]

(using [tex](a+b)(a-b)=a^2-b^2[/tex])

[tex]\frac{-2(\sqrt{x+y-2}+\sqrt{x+y+2})}{-4}[/tex]

[tex]\frac{\sqrt{x+y-2}+\sqrt{x+y+2}}{2}[/tex]

this is the required arrangement which result the expression by rationalizing