Question 402777

{{{(4x^4-4x^2-3)/(2x^2-3)}}}


first factor {{{(4x^4-4x^2-3)}}}:

replace {{{-4x^2}}} with {{{2x^2-6x^2}}}


{{{4x^4 + 2x^2 - 6x^2 -3}}}

Group the first two terms together and the last two terms together like this:

{{{(4x^4 + 2x^2) + (-6x^2-3)}}}

Factor a {{{2x^2}}} out of the first group and factor a {{{-3}}} out of the second group.

{{{2x^2(2x^2 + 1) + (-3)(2x^2 + 1)}}}

Now since we have a common term {{{(2x^2 + 1)}}} we can combine the two terms. 

{{{(2x^2 -3)(2x^2 + 1)}}}


so, now your expression will look like this:


{{{(2x^2 -3)(2x^2 + 1)/(2x^2-3)}}}


now, reduce


{{{cross((2x^2 -3))(2x^2 + 1)/cross((2x^2-3))}}}


{{{(2x^2 + 1)}}}