Mathematics: Which choice is equivalent to the fraction below when x = 2

Which choice is equivalent to the fraction below

Ответ:

kenzie9493

08.07.2021

B. $2( \sqrt{x} + \sqrt{x - 2} )$ ✅

Step-by-step explanation:

$\frac{4}{ \sqrt{x} - \sqrt{x - 2} } \\\\ = \frac{4}{ \sqrt{x} - \sqrt{x - 2} } \times \frac{ \sqrt{x} + \sqrt{x - 2} }{ \sqrt{x} + \sqrt{x - 2} } \\ \\ = \frac{4( \sqrt{x}) + 4( \sqrt{x - 2} )}{( { \sqrt{x} )}^{2} - { (\sqrt{x - 2} })^{2} } \\ \\ [∵(a + b)(a - b) = {a}^{2} - {b}^{2} ] \\ \\ = \frac{4 \sqrt{x} + 4 \sqrt{x - 2} }{x - (x - 2)} \\ \\ = \frac{4 \sqrt{x} + 4 \sqrt{x - 2} }{x - x + 2} \\ \\ = \frac{4( \sqrt{x} + \sqrt{x - 2} ) }{ 2} \\ \\= 2( \sqrt{x} + \sqrt{x - 2} )$

$\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}$

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Ответ:

alyssamaize

28.01.2020

Mathematics

The correct answer is: [B]: " True ".

Note: From visual inspecton of the graph shown — [Note: all images attached refer to the same graph.] :

→ We can see that when "x = -2" ; there is only one value for "y" ; and then the "line" of the graph stops for any coordinate corresponding to any "x-value" LESS THAN "-2" ;

→ and that there are corresponding "y-coordinates" corresponding to any "x-value that is equal to "-2" and "GREAT THAN "-2" .

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Which choice is equivalent to the fraction below when x >= 2

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