Question 187629
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I think you left off the 2 coefficient and also you left
the square root symbol off of the 7 in what you 
multiplied by.

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

To find out what to multiply by,
take the denominator, {{{2sqrt(3)+sqrt(7)}}}
Change the sign of the SECOND term, so that
you have {{{2sqrt(3)-sqrt(7)}}}  

Now put that over itself:{{{(2sqrt(3)-sqrt(7))/(2sqrt(3)-sqrt(7))}}}
so that it will just equal to 1 and therefore
it won't affect the value of the original 
problem when we multiply by it.

{{{(sqrt(2)-2) / (2sqrt(3)+sqrt(7))}}}{{{"×"}}}{{{(2sqrt(3)-sqrt(7)) / (2sqrt(3)-sqrt(7))}}}

Put parentheses around all numerators and denominators:

{{{((sqrt(2)-2)) / ((2sqrt(3)+sqrt(7)))}}}{{{"×"}}}{{{((2sqrt(3)-sqrt(7))) / ((2sqrt(3)-sqrt(7)))}}}

Indicate the multiplication of the numerators and
denominators, so that we just have one fraction:

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

FOIL out the top and bottom:

{{{ ( 2sqrt(6)-sqrt(14)-4sqrt(3)-2sqrt(7) )/  (4sqrt(9)-2sqrt(21)+2sqrt(21)-sqrt(49)) }}}


The middle two tems in the bottom cancel out:

{{{ ( 2sqrt(6)-sqrt(14)-4sqrt(3)-2sqrt(7) )/  (4sqrt(9)-cross(2sqrt(21))+cross(2sqrt(21))-sqrt(49)) }}}

Take square roots of 9 and 49, which are 3 and 7:

{{{ ( 2sqrt(6)-sqrt(14)-4sqrt(3)-2sqrt(7) )/  (4*3-7) }}}
{{{ ( 2sqrt(6)-sqrt(14)-4sqrt(3)-2sqrt(7) )/  (12-7) }}}
{{{ ( 2sqrt(6)-sqrt(14)-4sqrt(3)-2sqrt(7) )/5 }}}

Edwin</pre>