Question 1135698
1- indicates the quotient and remainder 

{{{(8x^3+4x-5)/(2x+1 )}}}...use long division

..............({{{4x^2-2x+3}}}
{{{2x+1}}}..|{{{8x^3+0*x^2+4x-5}}}
.....................{{{8x^3+4x^2}}}....subtract
...............................{{{-4x^2+4x}}}
.................................{{{-4x^2-2x}}}....subtract
............................................{{{6x-5}}}
.............................................{{{6x+3}}}....subtract
.................................................{{{-8}}}
the quotient is {{{4x^2-2x+2}}} 
and remainder is {{{-9}}}

{{{(8x^3+4x-5)/(2x+1 )=(4x^2-2x+3)(2x+1 )-8}}}



2- simplify the following radical expression: 

{{{(3+sqrt(5))/(sqrt(7)-sqrt(3))}}}...multiply both numerator and denominator by {{{(sqrt(7)+sqrt(3))}}}

{{{((3+sqrt(5))(sqrt(7)+sqrt(3)) )/((sqrt(7)-sqrt(3))(sqrt(7)+sqrt(3)))}}}

{{{(3sqrt(7)+sqrt(7)sqrt(5)+3sqrt(3)+sqrt(5)sqrt(3)) /((sqrt(7))^2-(sqrt(3))^2)}}}

{{{(3sqrt(7)+sqrt(7)sqrt(5)+3sqrt(3)+sqrt(5)sqrt(3)) /(7-3)}}}

{{{(3sqrt(7)+sqrt(35)+3sqrt(3)+sqrt(15)) /4}}}-> exact solution

if we go further approximate solution is {{{5.7306}}}


3-

{{{((x^3-y^3)/(2x^2-2y^2))*(( y^2+2xy+x^2)/(x^2+xy+y^2))}}}


{{{(((x - y) (x^2 + x y + y^2))/2(x^2-y^2))*((y+x)^2/(x^2+xy+y^2))}}}


{{{(((x - y) (x^2 + x y + y^2))/2((x-y)(x+y)))*((y+x)^2/(x^2+xy+y^2))}}}


{{{((cross((x - y)) cross((x^2 + x y + y^2))1)/2(cross((x-y))cross((x+y))))*((y+x)^cross(2)/cross((x^2+xy+y^2)))}}}


{{{(1/2)*(( y+x)/1)}}}


{{{( y+x)/2}}}