Question 248888
your equation is:


{{{(2*sqrt(2) + 1) / (-5*sqrt(2) + 3)}}}


the conjugate of the denominator would be {{{(-5*sqrt(2) - 3)}}}


multiply the expression by {{{(-5*sqrt(2) - 3) / (-5*sqrt(2) - 3)}}} to get:


{{{((2*sqrt(2) + 1) * (-5*sqrt(2) - 3)) / ((-5*sqrt(2) + 3) * (-5*sqrt(2) - 3))}}}


perform the indicated operations to get:


{{{(-23 - 11*sqrt(2)) / 41}}}


you got the denominator ok.


you got pieces of the numerator ok but something went wrong somewhere.


the numerator became:


{{{((2*sqrt(2) + 1) * (-5*sqrt(2) - 3))}}}


multiplying these terms together you would get:


{{{2*sqrt(2) * -5*sqrt(2) = -10*sqrt(2)^2 = -10*2 = -20}}}
{{{2*sqrt(2) * -3 = -6*sqrt(2)}}}
{{{1 * -5*sqrt(2) = -5*sqrt(2)}}}
{{{1 * -3 = -3}}}


combining like terms you would get {{{(-23-11*sqrt(2))}}}


your answer is {{{(-23-11*sqrt(2))/41}}}.