Simplify the rational expression. state any restrictions on the variable n^4-11n^2+30/ n^4-7n^2+10

To factor both numerator and denominator in this rational expression we are going to substitute  with ; so  and . This way we can rewrite the expression as follows:

Now we have two much easier to factor expressions of the form . For the numerator we need to find two numbers whose product is (30) and its sum  (-11); those numbers are -5 and -6.  and .
Similarly, for the denominator those numbers are -2 and -5.  and . Now we can factor both numerator and denominator:

Notice that we have  in both numerator and denominator, so we can cancel those out:

But remember than , so lets replace that to get back to our original variable:

Last but not least, the denominator of rational expression can't be zero, so the only restriction in the variable is 

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