Question 214925
Unfortunately, that is not the correct answer. You can use a calculator to find the approximations of the two expressions. If the expressions are close enough approximately, then chances are they are equal. In this case, I found that


{{{(2*sqrt(8)+7*sqrt(8))/(1-sqrt(2))=-61.45584}}} (approximately)


and 


{{{(9*sqrt(8)*(1-sqrt(2)))/3=-3.51472}}} (approximately)



So {{{(2*sqrt(8)+7*sqrt(8))/(1-sqrt(2))<>(9*sqrt(8)*(1-sqrt(2)))/3}}}




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To make things simpler, simplify the numerator {{{2*sqrt(8)+7*sqrt(8)}}} to get: {{{2*sqrt(8)+7*sqrt(8)=(2+7)*sqrt(8)=9*sqrt(8)=9*sqrt(4)*sqrt(2)=9*2*sqrt(2)=18*sqrt(2)}}}. I.e. {{{2*sqrt(8)+7*sqrt(8)=18*sqrt(2)}}}


So the expression {{{(2*sqrt(8)+7*sqrt(8))/(1-sqrt(2))}}} then becomes {{{(18*sqrt(2))/(1-sqrt(2))}}}





{{{(18*sqrt(2))/(1-sqrt(2))}}} Start with the given expression.



{{{((18*sqrt(2))/(1-sqrt(2)))((1+sqrt(2))/(1+sqrt(2)))}}} Multiply the fraction by {{{1+sqrt(2)}}}



{{{((18*sqrt(2))(1+sqrt(2)))/(1-sqrt(2))(1+sqrt(2)))}}} Combine the fractions.



{{{(18*sqrt(2)+18*sqrt(2)*sqrt(2))/(1-sqrt(2))(1+sqrt(2)))}}} Distribute



{{{(18*sqrt(2)+18*2)/(1-sqrt(2))(1+sqrt(2)))}}} Multiply



{{{(36+18*sqrt(2))/(1-sqrt(2))(1+sqrt(2)))}}} Rearrange the terms.



{{{(36+18*sqrt(2))/(1 - 2)}}} FOIL



{{{(36+18*sqrt(2))/(-1)}}} Combine like terms.



{{{-36-18*sqrt(2)}}} Reduce.



So {{{(18*sqrt(2))/(1-sqrt(2))=-36-18*sqrt(2)}}}



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Answer:



Since {{{(2*sqrt(8)+7*sqrt(8))/(1-sqrt(2))=(18*sqrt(2))/(1-sqrt(2))}}} this means that



{{{highlight((2*sqrt(8)+7*sqrt(8))/(1-sqrt(2))=-36-18*sqrt(2))}}}



which is our answer.




Check: take note that 


{{{(2*sqrt(8)+7*sqrt(8))/(1-sqrt(2))=-61.45584}}} (approximately)


and 


{{{-36-18*sqrt(2)=-61.45584}}} (approximately)



So this verifies our answer.