Rational Functions & Simplifying Rational Expressions

What is ? It would be . If , then

so the answer is .

*When dividing like bases , subtract exp onents .

Ex. 1

Ex. 2

Simplify if possible .

*A common mistake here it to try to reduce the and the x, the -16 and the 4. This would be incorrect. is a binomial that cannot be separated. However, whole factors can be divided out if possible. If we write the numerator and denominator in their prime factored form, we can rewrite the fraction this way : (notice that the denominator was a prime expression ). Now the x + 4 will factor out and the answer is x -4.

*When the denominator and numerator are factored, the fraction is written this way: . Again, take out the common factor and the answer is .