When

$\displaystyle t=\frac{{a^{2}+b^{2}}}{{a^{2}-b^{2}}}+

\frac{{a^{2}-b^{2}}}{{a^{2}+b^{2}}}$

express the following by using 't'

$\displaystyle \frac{{a^{8}+b^{8}}}{{a^{8}-b^{8}}}+

\frac{{a^{8}-b^{8}}}{{a^{8}+b^{8}}}$

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So,, I got this problem and the first thing I did was factoring

and I found the common denominator of 't'

Then it turned out that

$\displaystyle t=\frac{{2(a^{4}+b^{4})}}{{a^{4}-b^{4}}}$

Also I could change 'the follwing' into this.

$\displaystyle \frac{{2(a^{16}+b^{16})}}{{a^{16}-b^{16}}}$

Next, I tried dividing 'the following' by 't' so that I can find out what I should multiply to 't' to make it as 'the following'.

$\displaystyle \frac{{(a^{16}+b^{16})}({a^{4}-b^{4})}}{({a^{16}-b^{16})}({a^{4}+b^{4})}}$

.... And now I'm stuck.

I felt like I was getting closer to the answer but....

Any help would be appreciated..