Simplify the rational expression in the form A/B. X^-2+X^-4. Express the final result in a single fraction using positive exponents only.
x^-2+ x^-4
= 1/x^2 + 1/x^4
=(x^2 +1)/x^4
To simplify the rational expression (X^-2+X^-4), we need to find a common denominator for the two terms.
The first term, X^-2, can be rewritten as 1/X^2 and the second term, X^-4, can be rewritten as 1/X^4.
Now, to find the common denominator, we take the least common multiple (LCM) of X^2 and X^4, which is X^4.
We multiply the first term by X^2/X^2 and the second term by X^4/X^4 to obtain
(1/X^2) * (X^2/X^2) + (1/X^4) * (X^4/X^4)
= X^2/X^4 + 1/X^4
Now that we have a common denominator of X^4, we can combine the terms by adding the numerators:
(X^2 + 1)/X^4
And since we want the final result in a single fraction with positive exponents, we can simplify further by factoring the numerator:
(X^2 + 1) = (X + 1)(X - 1)
Thus, the final simplified rational expression is:
(X + 1)(X - 1)/X^4