Question 893815
{{{ (a^(-4)-b^(-4))/(a^(-2)-b^(-2)) }}}
Make the substitutions:
{{{ a^(-2) = 1/a^2 }}}
{{{ a^(-4) = 1/a^4 }}}
and
{{{ b^(-2) = 1/b^2 }}}
{{{ b^(-4) = 1/b^4 }}}
---------------------
{{{ ( 1/a^4 - 1/b^4 ) / ( 1/a^2 - 1/b^2 ) }}}
---------------------
Now multiply top and bottom by {{{ a^4b^4 }}}
{{{ (( a^4b^4 ) / ( a^4b^4 ))*(( 1/a^4 - 1/b^4 ) / ( 1/a^2 - 1/b^2 )) }}}
{{{ ( b^4 - a^4 ) / ( a^2b^4 - a^4b^2 ) }}}
{{{ (( b^2 - a^2 )*( b^2 + a^2 )) / (( a^2b^2 )*( b^2 - a^2 )) }}}
{{{ ( b^2 + a^2 ) / ( a^2b^2 ) }}}
{{{  b^2 / ( a^2b^2 ) + a^2 / ( a^2b^2 ) }}}
{{{ 1/a^2 + 1/b^2 }}}
or, 
{{{ a^(-2) + b^(-2) }}}
-----------------------
You can do a quick check by plugging
numbers into original and final answer, like
{{{ a = 3 }}}
{{{ b = 5 }}}
and use calculator
Hope this helps