Respuesta :

Edufirst
Answer: 

[tex]\frac{36+9 \sqrt{7} +4 \sqrt{2} + \sqrt{14} }{9}[/tex]

Explanation:


1) Expression given:

[tex] \frac{9+ \sqrt{2} }{4- \sqrt{7} } [/tex]

2) Rationalize by multiplying and dividing by the conjugate of the denominator


[tex] \frac{(9+ \sqrt{2} )}{(4- \sqrt{7} )} \frac{(4 + \sqrt{7} )}{(4+ \sqrt{7} )} [/tex]

3) Due the operations

[tex] \frac{9(4)+9 \sqrt{7} +4 \sqrt{2} + \sqrt{14} }{4^2-7} =[/tex]

[tex]\frac{36+9 \sqrt{7} +4 \sqrt{2} + \sqrt{14} }{9}[/tex]

Answer:

C on EDGE

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